The problem presents a formula for $a_n$, which is $a_n = a_1 \cdot r^{n-1}$. This is the formula for the $n$th term of a geometric sequence, where $a_1$ is the first term and $r$ is the common ratio.

1. Problem Description

The problem presents a formula for $a_n$, which is $a_n = a_1 \cdot r^{n-1}$. This is the formula for the $n$th term of a geometric sequence, where $a_1$ is the first term and $r$ is the common ratio.

2. Solution Steps

The formula given is:

$a_n = a_1 \cdot r^{n-1}$

This formula represents the $n$th term ($a_n$) of a geometric sequence, where $a_1$ is the first term of the sequence, $r$ is the common ratio between consecutive terms, and $n$ is the term number.

3. Final Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$.