#### Answer

$a_{n}=\frac{5}{2}(-\frac{1}{2})^{n-1}$
$a_{4}=-\frac{5}{16}$

#### Work Step by Step

We are given:
$a= \frac{5}{2}, r=- \frac{1}{2}$
We know that a geometric sequence has the form:
$a_{n}=ar^{n-1}$
Thus:
$a_{n}=\frac{5}{2}(-\frac{1}{2})^{n-1}$
And so:
$a_{4}= \frac{5}{2}*(-\frac{1}{2})^{3}=-\frac{5}{16}$