Solutions
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Question
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
Difficulty Level
MediumSolution
Option B is the correct answer.
Option Analysis
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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