<p>Can anyone give me the solution as well as explanation to this problem:</p>
<p>1, 2, 1, -1, -2,......
The first 5 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 3rd term can be obtained by subtracting the 1st term from the 2nd 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) 0</p>
<p>Here is my solution:</p>
<p>List out the first 6 numbers of the solution or until the cycle repeats:
1,2,1,-1,-2,-1 - These are the first 6 terms, and you also have to realise that this sequence of terms repeat over and over again in the overall sequence. (ie: the next 6 terms will be 1,2,1,-1,-2,-1 over again)</p>
<p>So find the sum of these six terms, which you will find to be 0, and since you want the first 36 terms (6 x 6 = 36) or (the sum of the first 6 terms x 6 = sum of first 36 terms)</p>
<p>(0 x 6 = 0) (A)</p>
<p>@etotheitimespi : thanks a lot. :)</p>