Answer
$a_{n} = (\frac{2}{5})(\frac{1}{5})^{n-1}$
Work Step by Step
Given Sequence is $\frac{2}{5},\frac{2}{25},\frac{2}{125},...$
$a_{1}= \frac{2}{5}$
$r = \frac{a_{2}}{a_{1}} = \frac{\frac{2}{25}}{\frac{2}{5}} = \frac{2}{25} \times \frac{5}{2} = \frac{1}{5}$
$a_{n} = a_{1} . r^{n-1}$
Substituting $a_{1}$ and $r$ values
$a_{n} = (\frac{2}{5})(\frac{1}{5})^{n-1}$
