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GRE Prep Club Team Member
Joined: 20 Feb 2017
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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7
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04 Jun 2021, 23:00
04 Jun 2021, 23:00
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\(S_n = 2S_{n-1} + 4\) and \(Q_n = 4Q_{n-1} + 8\) for all n > 1. If \(S_5 = Q_4\) and \(S_7 = 316\), what is the first value of n for which \(Q_n\) is an integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7
[#permalink]
05 Jun 2021, 11:22
05 Jun 2021, 11:22
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GeminiHeat wrote:
\(S_n = 2S_{n-1} + 4\) and \(Q_n = 4Q_{n-1} + 8\) for all n > 1. If \(S_5 = Q_4\) and \(S_7 = 316\), what is the first value of n for which \(Q_n\) is an integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
\(S_n = 2S_{n-1} + 4\)
\(S_7 = 316 = 2S_6 + 4\)
\(S_6 = 156\)
\(S_6 = 156 = 2S_5 + 4\)
\(S_5 = 76\)
Also, \(S_5 = Q_4\)
i.e. \(S_5 = 76 = 4Q_3 + 8\)
\(Q_3 = 17\)
\(Q_3 = 17 = 4Q_2 + 8\)
\(Q_2 = 2.25\)
Therefore the first value of \(n\) is 3 for which \(Q_n\) is an integer
Hence, option C
gmatclubot
Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7 [#permalink]
05 Jun 2021, 11:22
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