## Precalculus (6th Edition) Blitzer

$4,8,16,32,64,...$ Geometric
After observing the sequence carefully, we can notice that the difference between two consecutive terms is not the same. Thus, the common ratio will be determined as $4,8,16,32,64,...$ Here, ${{a}_{1}}=4,{{a}_{2}}=8,{{a}_{3}}=16,{{a}_{4}}=32,{{a}_{5}}=64,...$ Then, \begin{align} & \frac{{{a}_{2}}}{{{a}_{1}}}=\frac{8}{4} \\ & =2 \\ & \frac{{{a}_{3}}}{{{a}_{2}}}=\frac{16}{8} \\ & =2 \end{align} \begin{align} & \frac{{{a}_{4}}}{{{a}_{3}}}=\frac{32}{16} \\ & =2 \\ & \frac{{{a}_{5}}}{{{a}_{4}}}=\frac{64}{32} \\ & =2 \end{align} Therefore, the common ratio is 2. Hence the sequence is Geometric.