What is f (5) if f (1) = 3.2 and f (x+1) = 5/2?

Solution is given below

Step-by-step explanation:

f (x+1) = 2.5f (x) is an example of a recursion formula

Use what we know about f (1) to find f (2). Then use f (2) to find f (3), etc.

f (1) = 3.2

f (2) = f (1+1) = 2.5f (1) = 2.5 (3.2) = 8

f (3) = f (2+1) = 2.5f (2) = 2.5 (8) = 20

f (4) = f (3+1) = 2.5f (3) = 2.5 (20) = 50

f (5) = f (4+1) = 2.5f (4) = 2.5 (50) = 125

and for f (x+1) = 5/2

f (x + 1) = (5/2) (f (x))

f (1 + 1) = (5/2) (3.2)

f (2) = 8