[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}
\end{cases}\\\\
-------------------------------\\\\
a_1=3\qquad a_n=\left( \frac{1}{2} \right)a_{n-1}\impliedby
\begin{array}{llll}
\textit{simply means, to get the next term}\\
\textit{you multiply the previous, }a_{n-1},~by~\frac{1}{2}\\
meaning\qquad r=\frac{1}{2}
\end{array}
\\\\\\
a_n=3\cdot \left( \frac{1}{2} \right)^{n-1}[/tex]
