Answer
$4,8,16,32,64,...$ Geometric
Work Step by Step
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.
