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# A certain computer program generates a sequence of numbers

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Director
Joined: 08 Jul 2004
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A certain computer program generates a sequence of numbers [#permalink]

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23 Sep 2004, 14:46
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A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and ak = ak-1 + 2ak-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?

A. 32
B. 43
C. 64
D. 100
E. 128
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Director
Joined: 05 May 2004
Posts: 575
Location: San Jose, CA
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Kudos [?]: 61 [0], given: 0

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23 Sep 2004, 14:54
43

did by brut force i.e. enumeration
a1=1 a2=1
a3=a2+2*a1 = 3
a4=5 a=11 a6=21
a7=43
Director
Joined: 08 Jul 2004
Posts: 596
Followers: 2

Kudos [?]: 234 [0], given: 0

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25 Sep 2004, 05:05
The reason I posted was to know whether there is a smarter way .I guess no ?
Director
Joined: 31 Aug 2004
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25 Sep 2004, 09:36
I think there is no need to intuite any general formula since a7 is easy to assess. But if the question would have been a55 then try to add or alternate terms of the sequences (a1+a2+a3+a4...) or (a1-a2+a3-a4...), so that to emphasize a general rule.
25 Sep 2004, 09:36
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