Why Everyone Is Wrong Regarding Transgender Essay Topics

Why Everyone Is Wrong Regarding Transgender Essay Topics There's need to get around the practice as it does not permit students to unwind and concentrate on their studies for better academic outcomes. Long hours of mobile phone usage can cause elevated levels of stress. It isn't always simple to choose a thriving topic for preparing very good work. The more time spent on revising, the greater grade you will receive. Thus, unlike in the instance of different kinds which humans belong to, there's absolutely no external, observable evidence a male-bodied person is truly a woman. In truth, it is a very long practice. You should have your reasons, and our primary concern is that you wind up getting an excellent grade. It's crucial that you use the most suitable type of evidence, that you use it effectively, and that you've got an acceptable amount of it. In general, though equality is something everybody should strive for, in regards to sports and gender-based competitions, t here may be no middle ground between male and female. When discussing the term transgender, it's helpful to start by examining the notion of gender. In the modern society, gender means a lot more than it used to. A vital issue for transgender athletes is the difficulty of fitting into the two major kinds of sports competition. Below you'll find basic essentials of inclusion. Don't hesitate to incorporate all important info in the outline, and it's going to be useful in writing your document. When you summarize, you're offering a summary of a whole text, or no less than a lengthy section of a text. Write a comprehensive outline. A number of people may say such stereotypical things almost everyday and what they do not understand is they are brainwashing themselves. Conventional values have left others who don't belong behind and trying hard to survive. There are myriad reasons why most people today tell lies to others. Curiosity and attempting to understand another is ve ry good! People have family all over the world and with social media sites there's presently a way to find out what is happening in your family's everyday lives. Want to Know More About Transgender Essay Topics? If you would like to find the paper, don't hesitate to message me. Before starting gathering information for possible use as evidence in your argument, you should be certain that you comprehend the aim of your assignment. Put simply, you've got to spell out the importance of the evidence and its function in your paper. There are lots of ways to present your evidence. Choosing Good Transgender Essay Topics So in case you have been assigned with Essay Assignment on social issues then transgender rights is among the important elements of your subject. Dignity on paper has to be ensured in practice also. Taking essay outline help isn't that much crucial as finding a great essay for the topic that is primary. Until now, there's absolutely no law to protect trans indivi duals, since they are not included in the Sex Discrimination Ordinance. Robbery can happen almost anywhere at anytime, particularly on the streets. In the uk, a case was brought against the nation for violating a worldwide law. Many laws are looked at to safeguard the rights of Transgender individuals. Establishing such laws would allow transgender folks to reside in harmony with society and include them in modern life and it needs to be the target of all citizens to improve the life of others. Many countries don't allow individuals to modify the gender designation on their documents in any respect. The issues also have issues that exist around the world concerning gender. The American society as an illustration can demonstrate that religious fundamentalism plays an extremely significant role in the life span of transgender men and women. The MLDA ought to be lowered to age eighteen to coincide with those rights and duties and be able to aid benefit our nation. The Import ance of Transgender Essay Topics Genetic Engineering has the capability to benefit many folks. For Writing a Good Essay you require in order to choose superior topics. Transgender Essay Topics Fundamentals Explained Cis isn't a fake word and isn't a slur. Be aware that transgender doesn't have an ed at the end.

Penfolds Grange Brand Prism Free Essays

It was released in 1951 and kept it position for more than 50 years. But in 2009, Pinfold’s launched a special bottle, it was considered as a wrong action of it because that reduced the value of Grange. That is the reason our marketing plan is revitalization Grange, which will be launched in 2014. We will write a custom essay sample on Penfolds Grange Brand Prism or any similar topic only for you Order Now Before making a detail MIMIC plan, I will create the brand identity for Pinfold’s Grange relying on the brand identity prism of Seafarer (2008). ‘Brand identity prism’ is a diagrammatically analysis to identify one brand which is presented by a hexagonal prism. It illustrates that brand identify has six facets which are Physique, Personality, Culture, Relationship, Reflection and Self-image. Fanfold Grange is a vintage wine which is recognizable with a strong, distinctive, individual style record for cellaring performance. It is seen as an authentic voice of Australian fine wine and the strength of Pinfold’s winemaking culture and heritage. A brand has physique, according Keller, combines of either salient objective features (brand awareness) or emerging ones. Physique is not only backbone of brand but also its tangible added value. It may include product features, brand attributes and benefits. Simply, brand physique are basic things relying on it, customer can recognize and aware of the brand. The Pinfold’s Grange displays unique character and style and reflects the essence of Pinfold’s winemaking philosophy and provenance. It utilizes fully-ripe, intensely-favored and textured Shirrs grapes. It has an interesting history, an unbroken line of production since the very first vintage, consistent quality in each vintage, worldwide claim, longevity and limited production. Pinfold’s Grange is still loyal with the dark color, the design is quite simple and original but elegant with the sign of Pinfold’s which is the red Pinfold’s signature. Two main colors are white and red of the label which is not only for Grange but also or all lines of Pinfold’s and the early Grange label looked like a postage stamp – an attractive one. Although Pinfold’s is famous with many kinds of wine lines, Grange is still Australia’s most famous red wine regarded as Australia icon which most people have heard of or at least in passing. It was released in 1951 and kept it position for more than 50 years. This is a wonderfully opulent and a magic vintage. The Grange style is the original and most powerful expression of Pinfold’s multinational, multi- district, blending philosophy. Pinfold’s are the masters at understanding the power f an iconic sub-brand delivering a positive halo over the full brand range. Every year when the new vintage is released it becomes a media event of significant proportions. Pinfold’s Grange once again graced the prestigious Top 100 list of the US magazine ‘Wine Spectator’, having already been named in their Millennium edition as one of the ‘Top 100 wines’ of the 20th century. Granges have won 111 gold medals in shows, 63 silvers and 33 bronzes, 26 trophies and six championship awards, maybe seven or eight now. There are three Jimmy Watson trophies, in 1964, 1966 and 1968. All of these things make Grange’s reputation that every people can recall about it whenever they heard about it and it will be long lasting over the years. A brand has a personality. Personality is about what kind of person Grange would be if it were human including character and attitude. The human personality traits that are relevant for Pinfold’s Grange which are sophisticated, classic, elegant and reliable. Pinfold’s Grange is truly a unique brand from the first day it was released until now. A brand is a culture which takes a holistic view of the organization, its origins and the value it stands for. Every brand should have its own culture which is not only a concrete representation but also a means of communication and it is no doubt that Pinfold’s Grange really did it. Grange is the product of Australian culture regarded as the pride of Australian about one of the most famous wine in the world. If Frenchman is proud of their Champagne, to Australians, that is Grange-the Australia’s icon. Grange is not Just a symbol of luxury red wine in Australia, it is Australian image in the international wine market. Pinfold’s and Grange in particular is always representative of Australia now and in the future. Limited production and Just lease in a period of time also make the culture of Grange. The Grange fruit is from particular area, here is the grapes from Grange vineyard at Magical, South Australia. This is also a factor that makes Grange become special and have its own culture. Because Pinfold’s Grange is known as a luxury red wine line, the cultural facet is more meaningful in differentiating its brand which refers to its fundamental ideals and to its sets of values. A brand is a relationship: the strength of the relationship between the brand and customer. The Wall Street Journal has even published a DOD Jones Grange Index; the accompanying text was, ‘Wine lovers remember their first Grange the way they remember their first kiss! ‘. Pinfold’s’ advertisements carry the slogan â€Å"To those who do things for love not money’ and it’s also adapted to Grange. The relationship between Pinfold’s Grange and its customers are trust, consistent, dependability and exclusiveness. This is reflected by the loyalty of customers to their favorite wine brand. Grange was first released in 1951, but until now it is still the most famous wine and attract amount of number wine lovers who are willing wait for its new line ear by year despite the price rises and supply tensions, even promote this brand among others. It means that Fanfold Grange has built the trust and strong consistent in its customers’ mind by its quality and reputation themselves. Although Grange was launched in the market for more than five decades, it still has strong sales. The relationship between Pinfold’s Grange and its customers is also stronger because Pinfold’s always envelop its users with the image they want to signal to their social surroundings. A brand is a customer reflection. When mentioning about brand reflection, it is about he customer should be reflected as he or she wishes to be seen as a result of using a brand. Pinfold’s Grange is the sort of wine language for people who have deep pockets need to hear. Target segment of Pinfold’s is the customers who fall in medium and high disposable income, general from business background, have an average age of 35 plus, and are very loyal to a brand and aware of the wines in the market. In addition, these customers demand high quality wines with taste and texture. That is the reason why prestige, discerning and high social status are the thoughts of others to Grange lovers when they drink this wine. In addition, person who drinks Pinfold’s wine seems to be successful and looks like enjoying her/his successful life. A brand speaks to our self-image. Different from reflection which is how others see the brand’s users, self-image is the feeling of users themselves when they use the brand. Pinfold’s lovers in general and Grange in particular, feel confident and sophisticated when they drink this wine due to they are enjoying one of the most luxury and the highest quality in the world. Moreover, they feel special because we all know that with its luxurious and high-cost wine label, Pinfold’s Grange would push their grandmothers over for. And â€Å"it’s clearly cemented itself as a gift worthy of someone who’s Just been elected premier of Australia’s most populous state†. A customer might see himself fabulous and capable of drinking Pinfold’s Grange. Customers wish to display themselves that they are a part of community in which people have social approval, they are elegant, sophisticated and successful when they choose Pinfold’s Grange. In conclusion, this brand identity prism is a helpful tool in positioning Pinfold’s Grange in the wine market at the current time which help our group come up with a MIMIC plan for the release event of Grange in next October. How to cite Penfolds Grange Brand Prism, Papers

John Wilkes Resume free essay sample

To support the independence of the American colonies from England, and to support the liberties of mankind. Summary: I am an English politician, spokesman, and journalist of radical discontent. I am pro-Americanism and pro-separation from England. Firmly believe and support religious tolerance, freedom of the press, and Parliamentary reform. I inspire American Whig and other colonists with my attacks on King George Ill and the British government and by defending the berries of Englishmen.Some call me the champion of the powerless against the privileged. Once the American colonists declared their independence, my support for them decreased and I slowly became a more conservative politician. Professional Experience: 1757- Member Of Parliament for Lawlessly, I fought for religious liberties of Catholics and Protestants outside the Church of England. ; 1762- Published a weekly radical article called The North Briton ; 1 774. Admitted to the House of Commons to represent Middlesex and supported the rights of the voters rather than the House Major Accomplishments: Struck against government abuse of civil liberties by challenging general warrants ; 1763- Published The North Briton, No. We will write a custom essay sample on John Wilkes Resume or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page 45 attacking King George Ill on his speech regarding the Paris Peace Treaty of 1763, and was arrested for libel ; Denounced the Declaratory and Townsend Acts Taught people new ways to redress grievances using courts and publicParty leader of the London Radicals and an Idol of the London opinion ; Mob ; Inspired colonial Americans, with my fights against the government, to create the Bill Of Rights References: James Otis John Hancock Sam Adams John Adams Member of Bosons Sons of Liberty *The following men wrote letters to me regarding their grievances with the King, in hope I could help convince the government to reconsider their harsh policies, and thanking me for supporting the cause of liberty and mankind.

Accounting Ethics

Accounting Ethics Accounting EthicsWhen examining the effect of open marketing on the profession ofaccounting it is important to view it from three perspectives: theclient's, the profession's, and society's. Additionally, two key areasthat are affected by marketing must be addressed,these are concerning competition, and ethical implications. Marketing inpublic accounting is here to stay therefore making an argument against itsexistence would be fruitless; however, in order to achieve maximum benefitto the firm, the client, and s ociety more stringent guidelines must beimplemented at the firm level.The first, and most obvious, of the effected areas is competition.Within competition several points are discussed. First, the implicationsadvertising has on public accounting the model of perfect competitionversus the model of monopolistic compet ition. Secondly, the relationshipbetween firm size and advertising expenditures. Thirdly, the effect ofadvertising on firm specialization, the implications of clien t turnover onpublic accounting practice.CPA - LogoBefore making the comparison, a brief explanation why the two models are chosen is in order. Monopolistic competition has been chosen for the pre-advertising era because it most closely resembles the market structure in an extreme sense. The elements o f monopolistic competition are as follows: product differentiation, the presence of large numbers of sellers, and nonprice competition. Although accounting services between firms offer very little service differentiation, the absence of advertising serve s as a replacement because clients are not necessarily aware that other options are easily attainable. The post-advertising era is explained through the model of perfect competition for which the qualifications are as follows: very little or no service d ifferentiation, many sellers, and price as the only means of distinguishing one firms service from anothers.In a perfectly competitive market the price of a particular service is estab lished solely by the interaction of market...

Sequences on SAT Math Complete Strategy and Review

Sequences on SAT Math Complete Strategy and Review SAT / ACT Prep Online Guides and Tips A series of numbers that follows a particular pattern is called a sequence. Sometimes, each new term is found by adding or subtracting a certain constant, sometimes by multiplying or dividing. So long as the pattern is the same for every new term, the numbers are said to lie in a sequence. Sequence questions will have multiple moving parts and pieces, and you will always have several different options to choose from in order to solve the problem. We’ll walk through all the methods for solving sequence questions, as well as the pros and cons for each. You will likely see two sequence questions on any given SAT, so keep this in mind as you find your perfect balance between time strategies and memorization. This will be your complete guide to SAT sequence problemsthe types of sequences you’ll see, the typical sequence questions that appear on the SAT, and the best ways to solve these types of problems for your particular SAT test taking strategies. What Are Sequences? You will see two different types of sequences on the SATarithmetic and geometric. An arithmetic sequence is a sequence wherein each successive term is found by adding or subtracting a constant value. The difference between each termfound by subtracting any two pairs of neighboring termsis called $d$, the common difference. 14, 11, 8, 5†¦ is an arithmetic sequence with a common difference of -3. We can find the $d$ by subtracting any two pairs of numbers in the sequence, so long as the numbers are next to one another. $11 - 14 = -3$ $8 - 11 = -3$ $5 - 8 = -3$ 14, 17, 20, 23... is an arithmetic sequence in which the common difference is +3. We can find this $d$ by again subtracting pairs of numbers in the sequence. $17 - 14 = 3$ $20 - 17 = 3$ $23 - 20 = 3$ A geometric sequence is a sequence of numbers in which each new term is found by multiplying or dividing the previous term by a constant value. The difference between each termfound by dividing any neighboring pair of termsis called $r$, the common ratio. 64, 16, 4, 1, †¦ is a geometric sequence in which the common ratio is $1/4$. We can find the $r$ by dividing any pair of numbers in the sequence, so long as they are next to one another. $16/64 = 1/4$ $4/16 = 1/4$ $1/4 = 1/4$ Ready...set...let's talk sequence formulas! Sequence Formulas Luckily for us, sequences are entirely regular. This means that we can use formulas to find any piece of them we choose, such as the first term, the nth term, or the sum of all our terms. Do keep in mind, though, that there are pros and cons for memorizing formulas. Prosformulas provide you with a quick way to find your answers. You do not have to write out the full sequence by hand or spend your limited test-taking time tallying your numbers (and potentially entering them wrong into your calculator). Consit can be easy to remember a formula incorrectly, which would be worse than not having a formula at all. It also is an expense of brainpower to memorize formulas. If you are someone who prefers to work with formulas, definitely go ahead and learn them! But if you despise using formulas or worry that you will not remember them accurately, then you are still in luck. Most SAT sequence problems can be solved longhand if you have the time to spare, so you will not have to concern yourself with memorizing your formulas. That all being said, it’s important to understand why the formulas work, even if you do not plan to memorize them. So let’s take a look. Arithmetic Sequence Formulas $$a_n = a_1 + (n - 1)d$$ $$\Sum \terms = (n/2)(a_1 + a_n)$$ These are our two important arithmetic sequence formulas. We’ll look at them one at a time to see why they work and when to use them on the test. Terms Formula $a_n = a_1 + (n - 1)d$ This formula allows you to find any individual piece of your arithmetic sequencethe 1st term, the nth term, or the common difference. First, we’ll look at why it works and then look at some problems in action. $a_1$ is the first term in our sequence. Though the sequence can go on infinitely, we will always have a starting point at our first term. (Note: you can also assign any term to be your first term if you need to. We’ll look at how and why we can do this in one of our examples.) $a_n$ represents any missing term we want to isolate. For instance, this could be the 4th term, the 58th, or the 202nd. So why does this formula work? Imagine that we wanted to find the 2nd term in a sequence. Well each new term is found by adding the common difference, or $d$. This means that the second term would be: $a_2 = a_1 + d$ And we would then find the 3rd term in the sequence by adding another $d$ to our existing $a_2$. So our 3rd term would be: $a_3 = (a_1 + d) + d$ Or, in other words: $a_3 = a_1 + 2d$ If we keep going, the 4th term of the sequencefound by adding another $d$ to our existing third termwould continue this pattern: $a_4 = (a_1 + 2d) + d$ $a_4 = a_1 + 3d$ We can see that each term in the sequence is found by adding the first term, $a_1$, to a $d$ that is multiplied by $n - 1$. (The 3rd term is $2d$, the 4th term is $3d$, etc.) So now that we know why the formula works, let’s look at it in action. Now, there are two ways to solve this problemusing the formula, or simply counting. Let’s look at both methods. Method 1arithmetic sequence formula If we use our formula for arithmetic sequences, we can find our $a_n$ (in this case $a_12$). So let us simply plug in our numbers for $a_1$ and $d$. $a_n = a_1 + (n - 1)d$ $a_12 = 4 + (12 - 1)7$ $a_12 = 4 + (11)7$ $a_12 = 4 + 77$ $a_12 = 81$ Our final answer is B, 81. Method 2counting Because the difference between each term is regular, we can find that difference by simply adding our $d$ to each successive term until we reach our 12th term. Of course, this method will take a little more time than simply using the formula, and it is easy to lose track of your place. The test makers know this and will provide answers that are one or two places off, so make sure to keep your work organized so that you do not fall for bait answers. First, line up your twelve terms and then fill in the blanks by adding 7 to each new term. 4, 11, 18, ___, ___, ___, ___, ___, ___, ___, ___, ___ 4, 11, 18, 25, ___, ___, ___, ___, ___, ___, ___, ___ 4, 11, 18, 25, 32, ___, ___, ___, ___, ___, ___, ___ And so on, until you get: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81 Again, the 12th term is B, 81. Sum Formula $\Sum \terms = (n/2)(a_1 + a_n)$ Our second arithmetic sequence formula tells us the sum of a set of our terms in a sequence, from the first term ($a_1$) to the nth term ($a_n$). Basically, we do this by multiplying the number of terms, $n$, by the average of the first term and the nth term. Why does this formula work? Well let’s look at an arithmetic sequence in action: 10, 16, 22, 28, 34, 40 This is an arithmetic sequence with a common difference, $d$, of 6. A neat trick you can do with any arithmetic sequence is to take the sum of the pairs of terms, starting from the outsides in. Each pair will have the same exact sum. So you can see that the sum of the sequence is $50 * 3 = 150$. In other words, we are taking the sum of our first term and our nth term (in this case, 40 is our 6th term) and multiplying it by half of $n$ (in this case $6/2 = 3$). Another way to think of it is to take the average of our first and nth terms${10 + 40}/2 = 25$ and then multiply that value by the number of terms in the sequence$25 * 6 = 150$. Either way, you are using the same basic formula. How you like to think of the equation and whether or not you prefer $(n/2)(a_1 + a_n)$ or $n({a_1 + a_n}/2)$, is completely up to you. Now let’s look at the formula in action. Kyle started a new job as a telemarketer and, every day, he is supposed to make 3 more phone calls than the day previous. If he made 10 phone calls his first day, and he meets his goal, how many total phone calls does he make in his first two weeks, if he works every single day? 413 416 426 429 489 As with almost all sequence questions on the SAT, we have the choice to use our formulas or do the problem longhand. Let’s try both ways. Method 1formulas We know that our formula for arithmetic sequence sums is: $\Sum = (n/2)(a_1 + a_n)$ But, we must first find the value of our $a_n$ in order to use this formula. Once again, we can do this via our first arithmetic sequence formula, or we can find it by hand. As we are already using formulas, let us use our first formula. $a_n = a_1 + (n - 1)d$ We are told that Kyle makes 10 phone calls on his first day, so our $a_1$ is 10. We also know that he makes 3 more calls every day, for a total of 2 full weeks (14 days), which means our $d$ is 3 and our $n$ is 14. We have all our pieces to complete this first formula. $a_n = a_1 + (n - 1)d$ $a_14 = 10 + (14 - 1)3$ $a_14 = 10 + (13)3$ $a_14 = 10 + 39$ $a_14 = 49$ And now that we have our value for $a_n$ (in this case $a_14$), we can complete our sum formula. $(n/2)(a_1 + a_n)$ $(14/2)(10 + 49)$ $7(59)$ $413$ Our final answer is A, 413. Method 2longhand Alternatively, we can solve this problem by doing it longhand. It will take a little longer, but this way also carries less risk of incorrectly remember our formulas. As always, how you choose to solve these problems is completely up to you. First, let us write out our sequence, beginning with 10 and adding 3 to each subsequence number, until we find our nth (14th) term. 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49 Now, we can either add them up all by hand$10 + 13 + 16 + 19 + 22 + 25 + 28 + 31 + 34 + 37 + 40 + 43 + 46 + 49 = 413$ Or we can use our arithmetic sequence sum trick and divide the sequence into pairs. We can see that there are 7 pairs of 59, so $7 * 59 = 413$. Again, our final answer is A, 413. Only one more formula to go. Almost there! Geometric Sequence Formulas $$a_n = a_1( r^{n - 1})$$ (Note: while there is a formula to find the sum of a geometric sequence, but you will never be asked to find this on the SAT, and so it is not included in this guide.) As with the first arithmetic sequence formula, this formula will allow you to find any number of missing pieces, including your 1st term, your nth term, or your $r$. And, as always with sequences, you have the choice of whether to solve your problem longhand or with a formula. Method 1formula If you’re one for memorizing formulas, we can simply plug in our values into our equation in place of $a_n$, $n$, and $r$ in order to solve for $a_1$. We are told that Mr. Smith has 1 dollar 5 days later, which would be the 6th day (meaning our $n$ is 6), and that the ratio between each term is $1/4$. $a_n = a_1( r^{n - 1})$ $1 = a_1({1/4}^{6 - 1})$ $1 = a_1({1/4}^5)$ $1 = a_1(0.00097656)$ $1/0.00097656 = a_1$ $1024 = a_1$ So the 1st term in the sequence is 1024, which means that Mr. Smith starts with $1024 on Monday morning. Our final answer is 1024. Method 2longhand Alternatively, we can, as always, solve them problem by hand. First, set out our number of terms in order to keep track of them, with our 7th term, $1, last. ___, ___, ___, ___, ___, 1 Now, because our ratio is $1/4$ and we are working backwards, we must multiply each term by 4. (Why? Because ${1/{(1/4)} = 1 * 4$, according to the rules of fractions). ___, ___, ___, ___, 4, 1 ___, ___, ___, 16, 4, 1 And, if we keep going, we will eventually get: 1024, 256, 64, 16, 4, 1 Which means that we can see that our 1st term is 1024. Again, our final answer is 1024. As with all sequence solving methods, there are benefits and drawbacks to solving the question in each way. If you choose to use formulas, make very sure you can remember them exactly. And if you solve the questions by hand, be very careful to find the exact number of terms in the sequence. It can be all too easy to accidentally find one term more or fewer if you’re not carefully labeling or otherwise keeping track of your terms. I'm preeeeetty sure it's not a proper math formula unless mystery variables and exploding test tubes are involved somehow. Typical SAT Sequences Questions Because all sequence questions on the SAT can be solved without the use or knowledge of sequence formulas, the test-makers will only ever ask you for a limited number of terms or the sum of a small number of terms (usually 12 or fewer). As we saw above, you may be asked to find the 1st term in a sequence, the nth term, the difference between your terms (whether a common difference, $d$, or a common ratio, $r$), or the sum of your terms (in arithmetic sequences only). You also may be asked to find an unusual twist on a sequence question that combines your knowledge of sequences or your knowledge of sequences and other SAT math topics. For example: Again, let us look at both formulaic and longhand methods for how to solve a problem like this. Method 1formulas We are told that the ratio between the terms in our sequence is 2:1, successive term to previous term. This means that our common ratio is 2, as each term is being multiplied by 2 in order to find the next term. (Note: if you are not familiar with ratios, check out our guide to SAT ratios.) Now, we can find the ratio between our 8th and 5th terms in a few different ways, but the simplest waywhile still using formulasis simply to reassign our 5th term as our 1st term instead. This would then make our 8th term become our 4th term. (Why the 4th term? The 5th and 8th terms are 3 spaces from each other5th to 6th, 6th to 7th, and 7th to 8thwhich means our 1st term must be 3 spaces from our new nth term1st to 2nd, 2nd to 3rd, 3rd to 4th). Once we’ve designated our 5th term as our 1st term, we can use the strategy of plugging in numbers and assign a random value for our $a_1$. Then we will plug in our known values of $r$ (2) and $n$ (3) so that we can find our $a_n$. Let us call $a_1$ 4. (Why 4? Why not!) $a_n = a_1( r^{n - 1})$ $a_4 = 4(2^{4 - 1})$ $a_4 = 4(2^3)$ $a_4 = 4(8)$ $a_4 = 32$ So the ratio between our 4th term and our 1st term (the equivalent of the ratio to our 8th term and our 5th term) is: $32:4$ Or, when we reduce: $8:1$ The ratio between our 8th term and our 5th term is $8:1$ Our final answer is C, $8:1$. As you can see, this problem was tricky because we had to reassign our terms and use our own numbers before we even considered having to use our formulas. Let us look at this problem were we to solve it longhand instead. Method 2longhand If we choose to solve this problem longhand, we will not have to concern ourselves with reassigning our terms, but we will still have to understand that there are 3 spaces between our 8th and our 5th terms (8th to 7th, 7th to 6th, and 6th to 5th). Since we used the technique of plugging in our own numbers last time, let us use algebra for our longhand method. We know that each term is found by doubling the previous term. So let us say that our 5th term is $x$. ___, ___, ___, ___, x, ___, ___, ___ This would make our 6th term $2x$. ___, ___, ___, ___, x, 2x, ___, ___ And we can continue down the line until we get: ___, ___, ___, ___, x, 2x, 4x, 8x This means that our ratio between our 8th term and our 5th term is: $8x:x$ Or, in other words: $8:1$ Our final answer is, again, C, $8:1$. Again, you always have the choice to use formulas or longhand to solve these questions and how you prioritize your time (and/or how careful you are with your calculations) will ultimately decide which method you use. Now let's take a look at our SAT sequence question strategies. Tips For Solving Sequence Questions Sequence questions can be somewhat tricky and arduous to work through, so keep in mind these SAT math tips on sequences as you go through your studies: 1) Decide before test day whether or not you will use the sequence formulas Before you go through the effort of committing your formulas to memory, think about the kind of test-taker you are. If you are someone who loves to use formulas, then go ahead and memorize them now. Most sequence questions will go much faster once you have gotten used to using your formula. However, if you would rather dedicate your time and brainpower to other math topics or if you would simply rather solve sequence questions longhand, then don’t worry about your formulas! Don’t even bother to try to remember themjust decide here and now not to use them and save your mental energy for other pursuits. Unless you can be sure to remember themcorrectly, formulas will hinder more than help you on test day. So make the decision now to either memorize your formulas or forget about them entirely. 2) Write your values down and keep your work organized Though many calculators can perform long strings of calculations, sequence questions by definition involve many different values and terms. Small errors in your work can cause a cascade effect and one mistyped digit in your calculator can throw off your work completely. Even worse, you won’t know where the error happened if you do not keep track of your values. Always write down your values and label your terms in order to prevent a misstep somewhere down the line. 3) Keep careful track of your timing No matter how you solve a sequence question, these types of problems will generally take you more time than other math questions on the SAT. For this reason, most sequence questions are located in the last third of any particular SAT math section, which means the test-makers think of sequences as a â€Å"high difficulty† level problem. Time is your most valuable asset on the SAT, so always make sure you are using yours wisely. If you feel you can (accurately) answer two other math questions in the time it takes you to answer one sequence question, then maximize your point gain by focusing on the other two questions. Always remember that each question on the SAT math section is worth the same amount of points and you will get dinged if you get a question wrong. Prioritize both your quantity of answered questions as well as your accuracy, and don’t let your time run out trying to solve one problem. If you feel that you can answer a sequence problem quickly, go ahead! But if you feel it will take up too much time, move on and come back to it later (or skip it entirely, if you need to). No matter which method you choose to use, trust that you'll find the one that best suits your needs and abilities. Test Your Knowledge Now let’s test your sequence knowledge with real SAT math problems. 1) 2) What is the sum of the first 10 terms in the arithmetic sequence that begins:13, 21, 29,... 450 458 474 482 490 3) Answers: 200, E, 2035 Answer Explanations: 1) The number of squirrels triples every three years, so this is a geometric sequence. As always, we can either count longhand or use our formulas. Let’s look at each way. We first need to count how many times three years has passed between 1990 and 1999. Including the year 1990 and the year 1999, there are 4 terms for every 3 years between 1990 and 1999. 1990, 1993, 1996, 1999 This means that 1999 is our 4th term and 1990 is our 1st term. Now let’s plug in our values into our formula. $a_n = a_1( r^{n - 1})$ $5400 = a_1(3^{4-1})$ $5400 = a_1(3^3)$ $5400 = a_1(27)$ $200 = a_1$ Our first term is 200. There were 200 squirrels in 1990. Alternatively, we can simply find the number of squirrels in 1990 by counting by hand. Again, we need to find the number of groups of 3 years between 1990 and 1999, inclusive. 1990, 1993, 1996, 1999 Now, let us plug in our known value for 1999 and find the rest of our terms by dividing each term by 3. ___, ___, ___, 5400 ___, ___, 1800, 5400 And so on, until you get: 200, 600, 1800, 5400 Again, our first term is 200. There were 200 squirrels in 1990. 2) We are asked to find the sum of this arithmetic sequence, which means we can either use our formula or count our sequence by hand. Method 1formulas First, we need to determine our common difference, $d$, in the sequence. To do so, let us subtract one of our neighboring pairs of numbers. $21 - 13 = 8$ Before we can find our sum, however, we must find our $a_10$. This means we need to use our first arithmetic sequence formula: $a_n = a_1 + (n - 1)d$ $a_10 = 13 + (10 - 1)8$ $a_10 = 13 + 72$ $a_10 = 85$ Now that we know our $d$ and our $a_10$, we can plug in our values to find our sum. $(n/2)(a_1 + a_n)$ $(10/5)(13 + 85)$ $(5)(98)$ $490$ Our final answer is E, 490. Method 2counting If you do not want to remember or use your formulas, you can always find your answer by counting. First, we must still determine our $d$ by subtracting our neighboring terms: $29 - 21 = 8$ Now, we can find the value of all our terms by continuing to add 8 to each new term until we reach our 10th term. 13, 21, 29, ___, ___, ___, ___, ___, ___, ___ 13, 21, 29, 37, ___, ___, ___, ___, ___, ___ 13, 21, 29, 37, 45, ___, ___, ___, ___, ___ And so on, until we finally get: 13, 21, 29, 37, 45, 53, 61, 69, 77, 85 Now, we can either add them up individually ($13 + 21 + 29 + 37 + 45 + 53 + 61 + 69 + 77 + 85 = 490$), or you can, find your pairs of numbers, beginning from the outside in. We can see that there are 5 pairs of 98, so $5 * 98 = 450$ Our final answer is E, 490. 3) Because the price of our mystery item raises by $2 every year, this is an arithmetic sequence. Again, we have multiple ways to solve this kind of problemusing formulas, or counting longhand. Method 1formulas $a_n = a_1 + (n - 1)d$ $100 = 10 + (n - 1)2$ $100 = 10 + 2n - 2$ $100 = 8 + 2n$ $92 = 2n$ $n = 46$ Now, we know that 100 is the price at our 46th term, but this is not the same thing as 46 years from 1990. Remember: the number of terms from the 1st is always 1 fewer space than the actual count of the term. For instance, the 1st term in a sequence is 4 spaces from the 5th term and 5 spaces from the 6th term. Why? 1st to 2nd, 2nd to 3rd, 3rd to 4th, 4th to 5th. We can see it takes 4 total spaces to go from the 1st term to the 5th. For our price problem, our $n$ is 46, which means that the year will be $46 - 1 = 45$ actual spaces away from our starting term. So: $1990 + (46 - 1)$ $1990 + 45$ $2035$ The price will be $100 in 2035. Method 2counting Because each new term is determined by adding 2, it will take us a long time to get from 10 to 100. We can speed up this process by first finding the difference between the 1st and last term: $100 - 10 = 90$ And then we can divide this difference by the common difference, $d$: $90/2 = 45$ It will take 45 years to get to the price to raise to $100. 45 years after 1990 is: $1990 + 45$ $2035$ Again, the price will be $100 in 2035. Yeah! You toppled those sequence questions! The Take Aways Though sequence questions can take some little time to work through, they are usually made complicated by their number of terms and values rather than being actually difficult to solve. So long as you remember to keep all your work organized and decide before test-day whether or not you want to spend your study efforts memorizing, and you’ll be able to tackle any number of sequence questions the SAT can throw your way. As long as you keep your values straight (and don’t get tricked by bait answers!), you will be able to grind through these problems without fail. What’s Next? Now that you've taken on sequences and dominated, it's time to make sure you have a solid handle on the rest of your SAT math topics. The SAT presents familiar concepts in unfamiliar ways, so check out our guides on all your individual SAT topic needs. We'll provide you with all the strategies and practice problems on any SAT math topic you could ask for. Running out of time on SAT math? Not to worry! Our guide will show you how to maximize both your time and your score so that you can make the most of your time on test day. Don't know what score to aim for? Follow our simple steps to figure out what score is best for you and your needs. Looking to get a perfect score? Check out our guide to getting a perfect 800 on SAT math, written by a perfect-scorer! Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program.Along with more detailed lessons, you'll get thousands ofpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

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