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

Question

find the answer to f(5)=

 

Answer 1

Hi Phillip, f(5) would be 43. Here is the sequence:

 

f(1) = 3

 

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

 

f(3) = -2 * -5 + 1 = 11

 

f(4) = -2 * 11 + 1 = -21

 

f(5) = -2 * -21 + 1 = 43

 

Questions?

Answer 2

If f(n) = -2f(n-1), and you need to evaluate f(5), then we need to look at the the function like this.

 

f(5) = -2f(4)

f(4) = -2f(3)

f(3) = -2f(2)

f(2) = -2f(1)

 

Now, let's work this from the bottom up

f(2) = -2f(1) = -2(3) = -6  since we are told that f(1) = 3

f(3) = -2f(2) = -2(-6) = 12

f(4) = -2f(3) = -2(12) =-24

f(5) = -2f(4) = -2(-24) = 48

 

Hope this helps.