SL 1.3—Geometric Sequences

You've already seen arithmetic sequences, where you add (or subtract) a fixed number each time. Geometric sequences work differently , instead of adding, you multiply by a fixed value each time.

Geometric Sequence: A sequence in which each term is obtained by multiplying the previous term by a fixed constant called the common ratio, $r$.

The general form of a geometric sequence looks like this:

$u_1,u_{1}r,u_1{r}^2,u_1{r}^3,\dots ,u_1{r}^{n-1}$

where $u_1$ is the first term and $r$ is the common ratio.