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S_n=-1/S_{n-1}+1 for all integer values of n greater than 1. If S1 = 1
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16 Jul 2021, 22:33
16 Jul 2021, 22:33
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\(S_n=\frac{-1}{S_{n-1}+1}\) for all integer values of n greater than 1. If S1 = 1, what is the sum of the first 61 terms in the sequence?
(A) –48
(B) –31
(C) –29
(D) 1
(E) 30
(A) –48
(B) –31
(C) –29
(D) 1
(E) 30
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Re: S_n=-1/S_{n-1}+1 for all integer values of n greater than 1. If S1 = 1
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17 Jul 2021, 07:23
17 Jul 2021, 07:23
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Tip: In Sequence questions it is about finding the pattern which repeats so that we can reduce the problem to a smaller problem
\(S_n=\frac{-1}{S_{n-1}+1}\) and \(S_1\)=1
=> \(S_2=\frac{-1}{S_{2-1}+1}\) = \(\frac{-1}{S_1+1}\) = \(\frac{-1}{1+1}\) = \(\frac{-1}{2}\) = -0.5
=> \(S_3=\frac{-1}{S_2+1}\) = \(\frac{-1}{-0.5+1}\) = \(\frac{-1}{0.5}\) = -2
=> \(S_4=\frac{-1}{S_3+1}\) = \(\frac{-1}{-2+1}\) = \(\frac{-1}{-1}\) = 1
So, the sequence is
1, -0.5, -2, 1,...
So it is repeating after 3 numbers and sum of three numbers is 1 + -0.5 + -2 = -1.5
We need to find sum of 61 terms => 60 terms + 61\(61^{st}\) term
Sum of 60 terms = 20*(sum of three terms) = 20*-1.5 = -30
\(61^{st}\) term = 1 (as 60th term will be -2, last in the triplet of 1, -0.5, -2)
=> Sum of 61 terms = -30 + 1 = -29
So, answer will be C
Hope it helps!
To learn more about sequence, watch the following video
\(S_n=\frac{-1}{S_{n-1}+1}\) and \(S_1\)=1
=> \(S_2=\frac{-1}{S_{2-1}+1}\) = \(\frac{-1}{S_1+1}\) = \(\frac{-1}{1+1}\) = \(\frac{-1}{2}\) = -0.5
=> \(S_3=\frac{-1}{S_2+1}\) = \(\frac{-1}{-0.5+1}\) = \(\frac{-1}{0.5}\) = -2
=> \(S_4=\frac{-1}{S_3+1}\) = \(\frac{-1}{-2+1}\) = \(\frac{-1}{-1}\) = 1
So, the sequence is
1, -0.5, -2, 1,...
So it is repeating after 3 numbers and sum of three numbers is 1 + -0.5 + -2 = -1.5
We need to find sum of 61 terms => 60 terms + 61\(61^{st}\) term
Sum of 60 terms = 20*(sum of three terms) = 20*-1.5 = -30
\(61^{st}\) term = 1 (as 60th term will be -2, last in the triplet of 1, -0.5, -2)
=> Sum of 61 terms = -30 + 1 = -29
So, answer will be C
Hope it helps!
To learn more about sequence, watch the following video
gmatclubot
Re: S_n=-1/S_{n-1}+1 for all integer values of n greater than 1. If S1 = 1 [#permalink]
17 Jul 2021, 07:23
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