Answer
$\left\{
-2,-\dfrac{4}{3},-\dfrac{8}{9},-\dfrac{16}{26},-\dfrac{32}{81}
\right\}
$
Work Step by Step
With $a_1=-2$ and $r=\dfrac{2}{3}$, then,
\begin{array}{l}
a_2=a_1r\\
a_2=-2\left(\dfrac{2}{3}\right)\\
a_2=-\dfrac{4}{3}
,\\\\
a_3=a_2r\\
a_3=-\dfrac{4}{3}\left(\dfrac{2}{3}\right)\\
a_3=-\dfrac{8}{9}
,\\\\
a_4=a_3r\\
a_4=-\dfrac{8}{9}\left(\dfrac{2}{3}\right)\\
a_4=-\dfrac{16}{27}
,\\\\
a_5=a_4r\\
a_5=-\dfrac{16}{27}\left(\dfrac{2}{3}\right)\\
a_4=-\dfrac{32}{81}
\end{array}
Hence, the first five terms are $
\left\{
-2,-\dfrac{4}{3},-\dfrac{8}{9},-\dfrac{16}{26},-\dfrac{32}{81}
\right\}
.$
