Question

A sequence is defined recursively using the formula f(n + 1) = –0.5 f(n) . If the first term of the sequence is 120, what is f(5)? i need answer as soon as possible!

Answer 1

7.5
f(1) = 120
f(2) = -60
f(3) = 30
f(4) = -15
f(5) = 7.5

Answer 2

`f(5)=7.5`

Step-by-step explanation

The recursive definition is

`f(n+1)=-0.5f(n)`.

Since the first term of the sequence is given to us, we need to plug in
`n=1`.

This implies that;

`f(1+1)=-0.5f(1)`.

`f(2)=-0.5f(1)`

But we were given that,
`f(1)=120`.

This implies that;

`f(2)=-0.5* 120`

`f(2)=-60`

Since we now know that
`f(2)=-60`, we again plug in
`n=2` in to the recursive definition.

`f(2+1)=-0.5f(2)`

`\Righarrow f(3)=-0.5* -60`

`\Righarrow f(3)=30`.

We plug
`n=3` in to the formula again to determine the 4th term.

`f(4)=-0.5f(3)`.

`f(4)=-0.5 * 30`

`f(4)=-15`.

We finally find the 5th term by substituting
`n=4`.

`f(4+1)=-0.5f(4)`

`f(5)=-0.5* (-15)`

`f(5)=7.5`