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

Answer:

f(2) = 3

Step-by-step 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.