A geometric sequence with common ratio $r \neq 0$ is a sequence of numbers $s_{0}, s_{1}, s_{2}$, $\ldots$ that satisfies for any index $k, s_{k+1}=s_{k} \times r$. Determine an expression for $s_{n}$ in terms of $s_{0}, r$, and $n$.
We proceed exactly as before to establish $s_{n}=s_{0} r^{n}$ for all integers $n$.