## Precalculus (6th Edition) Blitzer

A sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant is called a geometric sequence. For example: $1,2,4,8,16\ldots$
A geometric sequence is the sequence in which each term after the first is obtained by multiplying the preceding term by a fixed nonzero constant. $a,ar,a{{r}^{2}},a{{r}^{3}},\cdots$. Consider the sequence, $1,2,4,8,16\ldots$ In the sequence given above, the common ratio between two consecutive terms 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 constant ratio.