Answer
False. The sequence is not geometric.
Work Step by Step
A series is said to be in geometric progression if the common ratio is the same, as shown below:
$\begin{align}
& \frac{{{a}_{2}}}{{{a}_{1}}}=\frac{{{a}_{3}}}{{{a}_{2}}} \\
& =\frac{{{a}_{4}}}{{{a}_{3}}}
\end{align}$
Here ${{a}_{1}}=2,{{a}_{2}}=6,{{a}_{3}}=24,{{a}_{4}}=120$.
So;
$\begin{align}
& \frac{{{a}_{2}}}{{{a}_{1}}}=\frac{{{a}_{3}}}{{{a}_{2}}} \\
& =\frac{{{a}_{4}}}{{{a}_{3}}} \\
& \frac{6}{2}=\frac{24}{6} \\
& =\frac{120}{24}
\end{align}$
It can be further solved as below:
$\begin{align}
& 3\ne 4 \\
& \ne 5
\end{align}$
Hence, the given statement is false.
For the statement to be true,
$\begin{align}
& \frac{{{a}_{2}}}{{{a}_{1}}}=\frac{{{a}_{3}}}{{{a}_{2}}} \\
& =\frac{{{a}_{4}}}{{{a}_{3}}}
\end{align}$
