Answer
The common ratio is $\frac{1}{4}$.
The fifth term is $-\frac{1}{32}$.
$a_{n} = -8(\frac{1}{4})^{n-1}$
Work Step by Step
The terms given are -8, -2, -$\frac{1}{2}$, -$\frac{1}{8}$ Since each term is multiplied by $\frac{1}{4}$ to get to the next, the common ratio is $\frac{1}{4}$. The fifth term = the fourth term $\times$ common ration = $-\frac{1}{8} \times \frac{1}{4} = -\frac{1}{32}$. The formula for the nth term of a geometric sequence is written in the form $a_{n} = a(r)^{n-1}$, since the first term (a) is -8 and the common ratio (r) is $\frac{1}{4}$.
Plug these into the formula to get $a_{n} = -8(\frac{1}{4})^{n-1}$
