If f(1) = 3f(1)=3 and f(n) = -2f(n-1) + 1f(n)=2f(n1)+1, what is f(5)f(5)?

1 Answer
Aug 6, 2016

f(5)=43f(5)=43

Explanation:

f(1)=3f(1)=3

f(n)=-2f(n-1)+1f(n)=2f(n1)+1

f(2)=-2f(1)+1f(2)=2f(1)+1

f(2)=-2(3)+1=-6+2=-5f(2)=2(3)+1=6+2=5

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

f(3)=-2(-5)+1f(3)=2(5)+1

f(3)=11f(3)=11

f(4)=-2(f(3))+1f(4)=2(f(3))+1

f(4)=-2(11)+1f(4)=2(11)+1

f(4)=-22+1=-21f(4)=22+1=21

f(5)=-2(f(4))+1f(5)=2(f(4))+1

f(5)=-2(-21)+1f(5)=2(21)+1

f(5)=42+1f(5)=42+1

f(5)=43f(5)=43