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

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30 Jun 2017, 13:38
00:00

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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Senior Manager
Joined: 28 Jun 2015
Posts: 290
Concentration: Finance
GPA: 3.5
Re: In a sequence a_1, a_2,…, each term after the first is found by taking  [#permalink]

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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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