Answer
$a_{n}=6\times \left( \dfrac {5}{3}\right) ^{n-1}$
Work Step by Step
$a_{n}=a\times r^{n-1};a_{m}=a\times r^{m-1}$
$\dfrac {a_{n}}{a_{m}}=\dfrac {r^{n}}{r^{m}}=r^{n-m}$
$\dfrac {a_{5}}{a_{2}}=r^{5-2}=\dfrac {\left( \dfrac {1250}{27}\right) }{10}\Rightarrow \dfrac {125}{27}=r^{3}\Rightarrow r=\dfrac {5}{3}$
$\dfrac {a_{n}}{a_{2}}=\left( r\right) ^{n-2}=\dfrac {a_{n}}{10}=\left( \dfrac {5}{3}\right) ^{n-2}=\left( \dfrac {5}{3}\right) ^{n}\times \left( \dfrac {3}{5}\right) ^{2}\Rightarrow a_{n}=10\times \left( \dfrac {3}{5}\right) ^{2}\times \left( \dfrac {5}{3}\right) ^{n}=6\times \left( \dfrac {5}{3}\right) ^{n-1}$