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by dunkin77 » Sun Jun 17, 2007 9:01 am
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


I got it wrong..I think I did not understand the question well. Can anyone explain?
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by RM » Sun Jun 17, 2007 10:39 am
a1 = 1
a2 = 1
a3 = a2 + 2(a1) = 1 + 2(1) = 3
a4 = a3 + 2(a2) = 3 + 2(1) = 5
a5 = a4 + 2(a3) = 5 + 2(3) = 11
a6 = a5 + 2(a4) = 11 + 2(5) = 21
a7 = a6 + 2(a5) = 21 + 2(11) = 43

Answer B, 43
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