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A certain computer program generates a sequence of numbers

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Director
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A certain computer program generates a sequence of numbers [#permalink] New post 23 Sep 2004, 13:46
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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
See, the attachment please
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Director
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Re: PS Sequence [#permalink] New post 23 Sep 2004, 13:54
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
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 [#permalink] New post 25 Sep 2004, 04:05
The reason I posted was to know whether there is a smarter way .I guess no ?
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 [#permalink] New post 25 Sep 2004, 08:36
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.
  [#permalink] 25 Sep 2004, 08:36
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