## Precalculus (6th Edition) Blitzer

A sequence in which each term is obtained after the first by multiplying the preceding term by a fixed nonzero constant is called a geometric sequence. Let the sequence be, $1,2,4,8,16\ldots$ In the above sequence, the common ration 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} Therefore, the common ration is a fixed nonzero constant, which is 2 in this case. Hence, the amount which is multiplied each time is called the common ratio of the sequence.