Question

If a sequence is defined recursively by f(0)=3 and f(n+1)=-f(n)+5 for n>0 then f(2) is equal to

Answer 1

f(2) = 3

Explanation:

We have that,

The recursive formula of the sequence is
`f(n+1)=-f(n)+5`, n> 0.

Also,
`f(0)=3`.

Then, the next term is,
`f(1)=f(0+1)=-f(0)+5` i.e.
`f(1)=-3+5` i.e.
`f(1)=2`.

Thus, we have,

`f(2)=f(1+1)=-f(1)+5` i.e.
`f(2)=-2+5` i.e.
`f(2)=3`.

Thus, f(2) is 3.