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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4

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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7 = 316, what is the first value of n for which Qn is an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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New post 12 Jan 2012, 04:00
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enigma123 wrote:
Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 and S7 = 316, what is the first value of n for which Qn is an integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Any idea how to solve these guys? I have given up after scratching my head for a while.


Assuming I have understood the symbols used correctly answer is C- 3

S7 = 2S6 +4 = 316

S6 = 312/2 = 156 = 2S5 + 4

S5 = 152/2 = 76 = Q4

Q4 = 4Q3 + 8 = 76

Q3 = 68/4 = 17

Q3 = 4Q2 + 8 = 17

Q2 = 9/4 = 2.25

Q2 = 4Q1 + 8

Q1 will not be integer

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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New post 12 Jan 2012, 22:11
Many thanks kp1811. Really appreciate your help.
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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New post 28 Jan 2016, 02:56
Is there any shortcut for this question? It took me 4 mins to solve this question.
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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New post 16 Feb 2016, 23:14
I wonder,why is it 700 level que?
It is quite simple
it is given
\(2S_4=4Q_3+4\)
\(S_4=2[Q_3+1]\)....i

we have been given that S_7=316
from this we can calculate S_6 and then ultimately S_4
\(S_4=36\)
putting this in equ i
\(Q_3=17\) ...ans
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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4 [#permalink]

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New post 18 Feb 2016, 07:18
mahakmalik wrote:
I wonder,why is it 700 level que?
It is quite simple
it is given
\(2S_4=4Q_3+4\)
\(S_4=2[Q_3+1]\)....i

we have been given that S_7=316
from this we can calculate S_6 and then ultimately S_4
\(S_4=36\)
putting this in equ i
\(Q_3=17\) ...ans


I think it's because it is long to solve and you have a big chance to make mistakes while calculating given that we deal with big numbers

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Re: Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4   [#permalink] 18 Feb 2016, 07:18
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Sn = 2Sn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If S5 = Q4

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