Answer
$1,-3,9,-27,81,...$ Geometric.
Work Step by Step
When we observe the sequence carefully, we see that the difference between two consecutive terms is not the same.
Thus, the common ratio will be computed as $1,-3,9,-27,81,...$
Now, ${{a}_{1}}=1,{{a}_{2}}=-3,{{a}_{3}}=9,{{a}_{4}}=-27,{{a}_{5}}=81,...$
So,
$\begin{align}
& \frac{{{a}_{2}}}{{{a}_{1}}}=\frac{\left( -3 \right)}{1} \\
& =-3 \\
& \frac{{{a}_{3}}}{{{a}_{2}}}=\frac{9}{\left( -3 \right)} \\
& =-3
\end{align}$
$\begin{align}
& \frac{{{a}_{4}}}{{{a}_{3}}}=\frac{\left( -27 \right)}{9} \\
& =-3 \\
& \frac{{{a}_{5}}}{{{a}_{4}}}=\frac{81}{\left( -27 \right)} \\
& =-3
\end{align}$
Therefore, the common ratio is -3.
Hence, the sequence is Geometric.
