Answer
$a_{5}=a_{1}\times r^{4}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{4}=\dfrac {128}{81};$
$a_{n}=a_{1}\times r^{n-1}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{n-1}$
Work Step by Step
$r=\dfrac {\dfrac {32}{27}}{\dfrac {8}{9}}=\dfrac {\dfrac {8}{9}}{\dfrac {2}{3}}=\dfrac {\dfrac {2}{3}}{\dfrac {1}{2}}=\dfrac {9}{3};a_{1}=\dfrac {1}{2}\Rightarrow a_{5}=a_{1}\times r^{4}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{4}=\dfrac {128}{81};a_{n}=a_{1}\times r^{n-1}=\dfrac {1}{2}\times \left( \dfrac {4}{3}\right) ^{n-1}$
