Answer
$a_{1}=-2$,
$a_{2}=2$,
$a_{3}=-\displaystyle \frac{8}{3}$,
$a_{4}=4$,
$a_{10}=\displaystyle \frac{512}{5}$
Work Step by Step
$a_{1}=(-1)^{1}\displaystyle \frac{2^{1}}{1}=-2$,
$a_{2}=(-1)^{2}\displaystyle \frac{2^{2}}{2}=2$,
$a_{3}=(-1)^{3}\displaystyle \frac{2^{3}}{3}=-\frac{8}{3}$,
$a_{4}=(-1)^{4}\displaystyle \frac{2^{4}}{4}=4$,
$a_{10}=(-1)^{10}\displaystyle \frac{2^{10}}{10}=\frac{1024}{10}=\frac{512}{5}$