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# In a sequence a1, a2,…, each term after the first is found

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In a sequence a1, a2,…, each term after the first is found [#permalink]  21 Jun 2017, 12:53
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Question Stats:

51% (01:17) correct 48% (02:55) wrong based on 66 sessions

In a sequence $$a_{1}$$, $$a_{2}$$,…, each term after the first is found by taking the negative of the preceding term, and adding 1. If $$a_{1} = 2$$, what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101
[Reveal] Spoiler: OA

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Last edited by Carcass on 27 Dec 2018, 03:24, edited 1 time in total.
Edited by Carcass
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Re: In a sequence a1, a2,…, each term after the first is found [#permalink]  19 Sep 2017, 09:43
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KUDOS
The sequence is 2, -1, 2, -1, ... and so on. Thus, every two elements of the sequence sum to 1. If we need to compute the sum of the first 99 terms, we can divide it by 2 in order to get the number of couples which sum to 1. 99/2=49.5, thus there are 49 couples so that 49*1=49, and we have the sum of the first 98 terms. The 99 term, being odd, will be equal to 2, thus we just have to sum 49 and 2 to get 51. Answer C!
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Re: In a sequence a1, a2,…, each term after the first is found [#permalink]  04 Feb 2018, 01:33
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KUDOS
According to the questions,
a1=2
The sequence is a1+(-a1+1)+(a1-1+1)+.....
So we can get the sequence as follows:
2-1+2-1+... up to 99th term. So the answer is 49*2-49=49+2=51
Target Test Prep Representative
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Re: In a sequence a1, a2,…, each term after the first is found [#permalink]  18 May 2018, 10:07
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Expert's post
Carcass wrote:

In a sequence a1, a2,…, each term after the first is found by taking the negative of the preceding term, and adding 1. If a1 = 2, what is the sum of the first 99 terms?

(A) 49
(B) 50
(C) 51
(D) 99
(E) 101

a1 = 2

a2 = -1

a3 = 2

a4 = -1

a5 = 2

a6 = -1

We see that each odd/even pair sums to positive 1.

There are 49 even/odd pairs in the first 98 terms; hence, the sum is 49. Since a99 is an odd-numbered term, a99 = 2. So the sum of the first 99 terms is 49 + 2 = 51.

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Re: In a sequence a1, a2,…, each term after the first is found   [#permalink] 18 May 2018, 10:07
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