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In a sequence a1, a2,…, each term after the first is found
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Updated on: 27 Dec 2018, 03:24
Updated on: 27 Dec 2018, 03:24
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59% (01:36) correct
40% (02:22) wrong based on 230 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
Re: In a sequence a1, a2,…, each term after the first is found
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19 Sep 2017, 09:43
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!
Re: In a sequence a1, a2,…, each term after the first is found
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04 Feb 2018, 01:33
04 Feb 2018, 01:33
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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
So, C is the answer.
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
So, C is the answer.
