Question

Given the recursive function f(n) = f(n - 1) - 3 ; f(1) = 9 , what would be the first three terms of the sequence ?

Answer 1

The first three terms of the given sequence are:

`f(1)=9,f(2)=6\ and\ f(3)=3`

Explanation:

Given:

A recursive function is given as:

`f(n)=(f(n-1)-3`

The first term is
`f(1)=9`

We need to find the remaining two terms
`f(2)\ and\ f(3)`

In order to find
`f(2)\ and\ f(3)`, we put
`n=2` and
`n=3` and simplify the recursive function.

For
`n=2`, the recursive function is given as:

`f(2)=f(2-1)-3\\f(2)=f(1)-3\\f(2)=9-3=6........[\because f(1)=9]`

Therefore, the second term is
`f(2)=6`

For
`n=3`, the recursive function is given as:

`f(3)=f(3-1)-3\\f(3)=f(2)-3\\f(2)=6-3=3........[\because f(2)=6]`

Therefore, the third term is
`f(3)=3`

Hence, the first three terms of the given sequence are:

`f(1)=9,f(2)=6\ and\ f(3)=3`