functions f(5)

Question

If f(1) = 3 and f(n) = -2f(n-1) +1, then f(5)=

Answer 1

f(1)=3

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

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

f(1)=-2f(0)+1, 3=-2f(0)+1, 3-1=-2f(0), 2=-2f(0), -1=f(0)

f(0)=-1

f(1)=3

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

f(3)=-2f(3-1)+1, f(3)=-2f(2)+1, f(3)=-2(-5)+1, f(3)=10+1, f(3)=11

f(4)=-2f(4-1)+1, f(4)=-2f(3)+1, f(4)=-2(11)+1, f(4)=-22+1, f(4)=-21

f(5)=-2f(5-1)+1, f(5)=-2f(4)+1, f(5)=-2(-21)+1, f(5)=42+1, f(5)=43

f(5)=43  (answer)

Answer 2

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

f(3) = -2*f(2) + 1 = 10+1 = 11

etc. 

 

You will need to repeat this process to find f(4), and then use f(4) to find f(5).