if f(2)=3 and f(n+1)=4f(n)-5 then what is f(5)

Answer 1

This is one way to write a recursive definition of a function:

Base Case:

f(2) = 3

Recursive Case:

f(n+1) = 4 * f(n) - 5 for n > 2

"What is f(5) ?"

Use the definition starting with f(2) and going forward:

f(2) = 3

f(3) = 4*f(2) - 5 = 4*3 - 5 = 7

f(4) = 4*f(3) - 5 = 4*7 - 5 = 23

f(5) = 4*f(4) - 5 = 4*23 - 5 = 87

f(5) = 87

Answer 2

Just doing the substitution, we find that

f(3) = 7

f(4) = 23

f(5) = 87