Question

F(n) = -11 + 22(n = 1)

Complete the recursive formula of f(n).
f(1) =
f(n) = f(n - 1)+

Answer 1

`f(n)=f(n-1)+22`.

Explanation:

Note: In the given function it should be (n-1) instead of (n=1).

Consider the given function is

`f(n)=-11+22(n-1)`

It is the explicit form of an A.P.

For
`n=1`,

`f(1)=-11+22(1-1)=-11+0=-11`

For
`n=2`,

`f(2)=-11+22(2-1)=-11+22=11`

Common difference is

`d=a_2-a_1=11-(-11)=11+11=22`

The recursive formula of an A.P. is

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

Substitute
`d=22` in the above formula.

`f(n)=f(n-1)+(22)`

`f(n)=f(n-1)+22`

Therefore, required recursive formula is
`f(n)=f(n-1)+22`.