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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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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
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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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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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According to the questions, a1=2 The sequence is a1+(a1+1)+(a11+1)+..... So we can get the sequence as follows: 21+21+... up to 99th term. So the answer is 49*249=49+2=51 So, C is the answer.



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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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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 oddnumbered term, a99 = 2. So the sum of the first 99 terms is 49 + 2 = 51. Answer: C
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Re: In a sequence a1, a2,…, each term after the first is found
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18 May 2018, 10:07





