Answer
$243$
Work Step by Step
The first term is $a=\sqrt{3}$, and the common ratio is:
$\begin{align}
& r=\frac{{{a}_{2}}}{{{a}_{1}}} \\
& =\frac{3\sqrt{3}}{3} \\
& =\sqrt{3}
\end{align}$
So,
$r=\sqrt{3}$
Use ${{a}_{n}}=a{{r}^{n-1}}$.
$\begin{align}
& {{a}_{10}}=\sqrt{3}{{\left( \sqrt{3} \right)}^{10-1}} \\
& =\sqrt{3}{{\left( \sqrt{3} \right)}^{9}} \\
& ={{\left( \sqrt{3} \right)}^{10}}
\end{align}$
Hence,
$\begin{align}
& {{a}_{10}}={{\left( \sqrt{3} \right)}^{10}} \\
& =243
\end{align}$
Thus, the $10\text{th}$ term of the geometric sequence $\sqrt{3},3,3\sqrt{3},...$ is $243$.
