[tex]\bf \begin{array}{ccll}
n&term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1&a_1&a_1\\
2&a_2&6a_1\\
3&a_3&6(6a_1)\\
&&36a_1
\end{array}\implies \stackrel{\textit{3rd term is 24}}{36a_1=24}
\\\\\\
a_1=\cfrac{24}{36}\implies a_1=\cfrac{2}{3}[/tex]
[tex]\bf n^{th}\textit{ term of a geometric sequence}
\\\\
a_n=a_1\cdot r^{n-1}\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
r=6\\
a_1=\frac{2}{3}
\end{cases}
\\\\\\
\boxed{a_n=\cfrac{2}{3}\cdot 6^{n-1}}[/tex]
