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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # In a sequence a1, a2,…, each term after the first is found  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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GRE 1: Q160 V160 Followers: 315

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In a sequence a1, a2,…, each term after the first is found [#permalink]
Expert's post 00:00

Question Stats: 54% (01:13) correct 45% (02:26) wrong based on 133 sessions

Last edited by Carcass on 27 Dec 2018, 03:24, edited 1 time in total.
Edited by Carcass Director Joined: 03 Sep 2017
Posts: 518
Followers: 2

Kudos [?]: 440  , given: 66

Re: In a sequence a1, a2,…, each term after the first is found [#permalink]
1
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! Intern Joined: 08 Dec 2017
Posts: 40
Followers: 1

Kudos [?]: 46  , given: 70

Re: In a sequence a1, a2,…, each term after the first is found [#permalink]
1
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 Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 8

Kudos [?]: 202  , given: 0

Re: In a sequence a1, a2,…, each term after the first is found [#permalink]
1
KUDOS
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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews Re: In a sequence a1, a2,…, each term after the first is found   [#permalink] 18 May 2018, 10:07
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