Question

If f(1)=7 and f(n)=3f(n-1)+3 then find the value of (3)

Answer 1

Given:

`f(1)=7`

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

To find:

The value of f(3).

Solution:

We have,

`f(n)=3f(n-1)+3` ...(i)

Substituting
`n=2` in (i), we get

`f(2)=3f(2-1)+3`

`f(2)=3f(1)+3`

Substituting
`f(1)=7` in the above equation, we get

`f(2)=3(7)+3`

`f(2)=21+3`

`f(2)=24`

Now, substituting
`n=3` in (i), we get

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

`f(3)=3f(2)+3`

Substituting
`f(2)=24` in the above equation, we get

`f(3)=3(24)+3`

`f(3)=72+3`

`f(3)=75`

Therefore, the value of f(3) is 75.