Answer
It is a geometric sequence.
$r=-\frac{1}{3}$
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:
$\frac{a_2}{a_1}=\frac{-9}{27}=-\frac{1}{3}$
$\frac{a_3}{a_2}=\frac{3}{-9}=-\frac{1}{3}$
$\frac{a_4}{a_3}=\frac{-1}{3}=-\frac{1}{3}$
It is a geometric sequence.
Common ratio: $r=-\frac{1}{3}$
