Question

A sequence is defined by the formula f(n + 1) = f(n) – 3. If f(4) = 22, what is f(1)?

Answer 1

The value of f(1)=31

Explanation:

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

f(4)=22

We need to find the f(1)

Put n=3 into recursion formula

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

`f(3)=22+3=25`

Put n=2 into recursion formula

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

`f(2)=25+3=28`

Put n=1 into recursion formula

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

`f(1)=28+3=31`

Hence, The value of f(1)=31