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