Geometric Sequences

A geometric sequence has a constant ratio between consecutive terms. If the ratio is $r$, then each term equals the previous term multiplied by $r$.

Example: $3, 6, 12, 24, 48, ...$ has $r = 2$. Each term is double the previous one.

The general formula is $a_n = a_1 \times r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio. For our example, $a_n = 3 \times 2^{n-1}$.