Question

if a sequence is defined recursively by f(0 ) = 3 and f(n+1) = -f(n)+5 for n is equal to or greater than 0, then f(2) is equal to?

Answer 1

if f(n+1)= -f(n) +5
then f(2)=-f(1)+5
we don't know f(1) yet. Use the same rule as above:
f(1)=-f(0)+5, we do know that f(0)=3, so f(1)=-3+5=2
so f(2)=-f(1)+5=-2+5=3

Answer 2

value of f(2) is, 3

Explanation:

As per the statement::

`f(0) = 3`

and recursive formula is given as:

`f(n+1) = -f(n)+5` .....[1]
`n\geq 0`

To find the value of f(2):

Substitute n = 0 in [1] we have;

`f(1) = -f(0)+5`

⇒
`f(1) = -3+5 = 2`

⇒
`f(1) = 2`

Now. substitute n =1 we have;

`f(2) = -f(1)+5`

⇒
`f(2) = -2+5 = 3`

⇒
`f(2) = 3`

Therefore, the value of f(2) is, 3