SOLUTION: If a sequence is defined recursively by f(0)=2 and f(n+1)=-2f(n)+3 for n>or=0 then f(2) is equal to?

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Question 1131897: If a sequence is defined recursively by f(0)=2 and f(n+1)=-2f(n)+3 for n>or=0
then f(2) is equal to?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


f(0)=2; for n >= 0, f(n+1) = -2*f(n)+3.

Set n = 0 in the recursive definition to find f(1):
n=0: f(1) = -2*f(0)+3 = -2(2)+3 = -4+3 = -1

Set n = 1 in the recursive definition to find f(2):
n=1: f(2) = -2*f(1)+3 = -2(-1)+3 = 2+3 = 5

ANSWER: f(2) = 5