Answer
$2.5(1-0.6^n)$.
Work Step by Step
$\frac{a_3}{a_2}=\frac{\frac{9}{25}}{\frac{3}{25}}=\frac{a_2}{a_1}=\frac{\frac{3}{5}}{1}=\frac{3}{5}=r$, thus this is a geometric sequence with a common ratio of $\frac{3}{5}$
The nth term of a geometric sequence can be obtained by the following formula: $a_n=a_1(r^{n-1})$, where $a_1$ is the first term and $r$ is the common ratio.
The sum of a geometric sequence until $n$ can be obtained by the formula $S_n=a_1(\frac{1-r^n}{1-r})$ where $a_1$ is the first term and $r$ is the common ratio. Hence here the sum is: $S_n=1(\frac{1-0.6^n}{1-0.6})=2.5(1-0.6^n)$.
