Answer
It is a geometric sequence.
$r=-3$
Work Step by Step
A sequence is geometric if $\frac{a_2}{a_1}=\frac{a_3}{a_2}=\frac{a_4}{a_3}=...=r$
For the given sequence we have that:
$\frac{a_2}{a_1}=\frac{-\frac{3}{5}}{\frac{1}{5}}=-\frac{3}{5}\frac{5}{1}=-3$
$\frac{a_3}{a_2}=\frac{\frac{9}{5}}{-\frac{3}{5}}=-\frac{9}{5}\frac{5}{3}=-3$
$\frac{a_4}{a_3}=\frac{-\frac{27}{5}}{\frac{9}{5}}=-\frac{27}{5}\frac{5}{9}=-3$
It is a geometric sequence.
Common ratio: $r=-3$
