 It is currently 26 Jun 2019, 02:50 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 7019
Followers: 117

Kudos [?]: 1369 , given: 6383

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

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

_________________

Last edited by Carcass on 27 Dec 2018, 03:24, edited 1 time in total.
Edited by Carcass Director Joined: 03 Sep 2017
Posts: 520
Followers: 1

Kudos [?]: 358  , 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 [?]: 43  , 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: 5

Kudos [?]: 140  , 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
Display posts from previous: Sort by

In a sequence a1, a2,…, each term after the first is found  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.