Answer
$a_n=\dfrac{1}{3}a_{n-1}$
Work Step by Step
Let $a_n$ be our recursive sequence. WE need to find the first term and the rule showing how we obtain the general term using one (or more) of the terms before it.
We notice that we have:
$$\begin{align*}
a_1&=324\\
a_2&=108=\dfrac{324}{3}\\
a_3&=36=\dfrac{108}{3}\\
a_4&=12=\dfrac{36}{3}\\
a_5&=4=\dfrac{12}{3}.
\end{align*}$$
Therefore we got:
$$\begin{cases}
a_1&=324\\
a_n&=\dfrac{1}{3}a_{n-1}.
\end{cases}$$
The recursive rule is:
$$a_n=\dfrac{1}{3}a_{n-1}.$$
