Answer
It is a geometric sequence.
$r=\frac{2}{\sqrt 3}$
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:
$\frac{a_2}{a_1}=\frac{\frac{4}{\sqrt 3}}{2}=\frac{2}{\sqrt 3}$
$\frac{a_3}{a_2}=\frac{\frac{8}{3}}{\frac{4}{\sqrt 3}}=\frac{8}{3}.\frac{\sqrt 3}{4}=\frac{2(4)(\sqrt 3)}{\sqrt 3(\sqrt 3)(4)}=\frac{2}{\sqrt 3}$
$\frac{a_4}{a_3}=\frac{\frac{16}{3\sqrt 3}}{\frac{8}{3}}=\frac{16}{3\sqrt 3}\frac{3}{8}=\frac{2(8)(3)}{3(\sqrt 3)(8)}=\frac{2}{\sqrt 3}$
It is a geometric sequence.
Common ratio: $r=\frac{2}{\sqrt 3}$
