Question

F(n) = 93 + 4(n − 1)

Complete the recursive formula of f(n).

f(1) =_____

f(n) = f(n − 1)+____

Answer 1

`f(1) = 93`,
`f(n) = f(n-1) +4`

Explanation:

The value of f(1) is:

`f(1) = 93 +4\cdot (1-1)`

`f(1) = 93`

The values for n and n-1, are respectively:

`f(n-1) = 93 + 4\cdot (n-2)`

`f(n) = 93 + 4\cdot (n-1)`

After some algebraic manipulation, the following expression is obtained:

`f(n) = 93 + 4\cdot (n-2) + 4`

`f(n) = f(n-1) +4`