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In a sequence a_1, a_2,…, each term after the first is found by taking

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Manager
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Joined: 24 Dec 2016
Posts: 62
Location: United States
Concentration: Statistics
Schools: Duke Fuqua
GMAT 1: 720 Q49 V40
GPA: 3.38
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In a sequence a_1, a_2,…, each term after the first is found by taking  [#permalink]

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New post 30 Jun 2017, 13:38
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

74% (02:20) correct 26% (02:50) wrong based on 51 sessions

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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

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Re: In a sequence a_1, a_2,…, each term after the first is found by taking  [#permalink]

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New post 30 Jun 2017, 19:31
1
\(a_1 = 2\)
\(a_2 = -2+1 = -1\)
\(a_3 = -(-1)+1 = 2\)
\(a_4 = -2+1 = -1\)
\(a_5 = -(-1)+1 = 2\), and the pattern continues.

Every odd number in the sequence is \(2\), and every even number is \((-1)\).

There are 50 \(2s\) and 49 \(1s\) in the sequence, so their sum will be = \(50*2 + 49*(-1) = 100 - 49 = 51\). Ans - C.
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Re: In a sequence a_1, a_2,…, each term after the first is found by taking   [#permalink] 30 Jun 2017, 19:31
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