## Precalculus (6th Edition) Blitzer

The amount by which we multiply each time is called the common ratio of the sequence. The general form of the geometric sequence is $a,ar,a{{r}^{2}},a{{r}^{3}},\cdots$. And $r$ is the common ratio.
The geometric sequence is the sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant ($r$). $a,ar,a{{r}^{2}},a{{r}^{3}},\cdots$. Consider the sequence, $1,2,4,8,16\ldots$ In the sequence given above, the common ratio between two consecutive term is constant. For example, \begin{align} & \frac{2}{1}=\frac{4}{2} \\ & =\frac{8}{4} \\ & =\frac{16}{8} \\ & =2 \end{align} So, 2 is the fixed nonzero common ratio.