Find the term of a geometric sequence Exercise

Find the general term of the geometric sequences defined as follows.

\(\displaystyle{4, \dfrac{-8}{3},\dfrac{16}{9},\dfrac{-32}{27},\dfrac{64}{81}, …}\)

\(\displaystyle{2, 6, 18, 54, 162, ...}\)

\(\displaystyle{6, -\dfrac{9}{2}, \dfrac{27}{8}, -\dfrac{81}{32},...}\)

\(\displaystyle{\dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}, \dfrac{1}{16},\dfrac{1}{32}...}\)

\(\displaystyle{6, -12, 24, -48, 96,...}\)

\(\displaystyle{-4,-5,-\dfrac{25}{4},-\dfrac{125}{16},...}\)

\(\displaystyle{27, 18, 12, 8, \dfrac{16}{3},...}\)