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

ANSWER

$f(5)=7.5$

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;

$f(2)=-0.5\times 120$

$f(2)=-60$

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

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

$\Righarrow f(3)=-0.5\times -60$

$\Righarrow f(3)=30$.

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

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

$f(4)=-0.5 \times 30$

$f(4)=-15$.

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

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

$f(5)=-0.5\times (-15)$

$f(5)=7.5$