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what is the first value of n

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what is the first value of n

by abhi332 » Wed Feb 24, 2010 12:16 pm
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

[spoiler]OA: C[/spoiler]
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by DeepthiRajan » Wed Feb 24, 2010 3:49 pm
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?

S7 = 2S6 +4
316=2S6+4
S6= 156

S6 = 2S5+4; Since S5=Q4
S6= 2Q4+4=2(4Q3+8) +4 = 8Q3+20
156 = 8Q3+20=> 136 = 8Q3
Q3=17

Q3 = 4Q2+8
17= 4Q2+8 => Q2=17-9/4 which is not an integer, so is Q1 therefore, the first value for Qn is integer is 3 (Q3 ), hence C
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