Answer
It is a geometric sequence.
$r=-\sqrt 7$
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:
$\frac{a_2}{a_1}=\frac{-\sqrt 7}{1}=-\sqrt 7$
$\frac{a_3}{a_2}=\frac{7}{-\sqrt 7}=\frac{7}{-\sqrt 7}\frac{\sqrt 7}{\sqrt 7}=\frac{7\sqrt 7}{-(\sqrt 7)^2}=\frac{7\sqrt 7}{-7}=-\sqrt 7$
$\frac{a_4}{a_3}=\frac{-7\sqrt 7}{7}=-\sqrt 7$
It is a geometric sequence.
Common ratio: $r=-\sqrt 7$
