<p>1, 2, 1, -1, -2</p>
<p>The first five terms of a sequence are shown above. After the second term, each term can be obtained by subtracting from the previous term the term before that. For example, the third term can be obtained by subtracting the first term from the second term. What is the sum of the first 36 terms of the sequence?</p>
<p>A) 0
B) 4
C) 12
D) 24
E) 30</p>
<p>The answer is A, but how do u do it?</p>
<p>with these problems, find a few more terms and a pattern should emerge</p>
<p>-2-(-1) = -1 (6th term) -1-(-2) = 1 (7th term)</p>
<p>note that the 7th term is the same as the 1st term, so the pattern repeats in groups of 6 terms. summing the first 6 terms, we get 0. since 36 is a multiple of 6, the answer is A)0.</p>
<p>First expand the sequence one more term, so you have a sequence of 6 terms and not 5. -1 would be the sixth term.</p>
<p>Then you find a pattern between these 6 terms, and the question states you subtract the pervious term by the next term. </p>
<p>It asks you for the sum of the first 36 numbers in the sequence. You have observed the sequence between the first 6. So this problem comes down to logic and arithmetic. </p>
<p>If you didn't know any algebra II, you could still solve this, and you wouldn't need a calculator either.</p>
<p>1 Systematically write out the sequence to 36 terms. Add all the terms together.
2 Use an algebra II sigma notation problem. The problem says you need to go to 36 terms. So k-> 36, you're solving for n, the formula is k[n + 1] - k[n] and plug in.</p>
<p>2 Use an algebra II sigma notation problem. The problem says you need to go to 36 terms. So k-> 36, you're solving for n, the formula is k[n + 1] - k[n] and plug in.</p>
<p>can u explain that part a little more please^^^^?</p>
<p>i'm not sure what amit is referring to, but patterns on the SAT math require a bit of logic to figure out. these problems are medium difficulty and should be solved quickly.</p>
<p>we have 1,2,1,-1,-2 it's easy to verify that after the second term, each term results from subtracting the previous two terms(2-1 = 1 = 3rd term, 1-2= -1 = 4th term, -1-1 = -2 = 5th term). Now the 6th term is -1. Finding few more terms KILLS SAT math problems. 7th term is -1--2 = 1, 8th term = 1--1=2. It's our original sequence! 9th term = 2-1 = 1... and so on</p>
<p>you could write out all 36 terms but that wouldn't be too good since this is probably a medium level question at best. sum of first 6 terms = 0, sum of next 6 = 0 and so on... A) 0</p>