The $n$-th term of a geometric series with first term $a$ and common ratio $r$ is —

In a geometric series each term is the previous one multiplied by the common ratio $r$, so the terms are $a, ar, ar^2, \dots$. Counting from $a=ar^0$, the $n$-th term carries the exponent $n-1$, giving $ar^{n-1}$.