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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 = ?

Option A:

32

Option B:

43

Option C:

64

Option D:

100

Option E:

128

Option B is the correct answer.

Ak= A(k-1) + 2* A(k-2)

A1= 1 and A2= 1

A(3)= A(3-1) + A(3-2)

=> = A(2) + 2(A1)

=> = 1 + 2*1 A(3)= 3

And with similar pattern,

A(4)= 3 + 2*1 = 5

A(5)= 5 + 2*3 = 11

A(6)= 11 + 2*5 = 21

A(7)= 21 + 2*11 = 43

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