Answer
Geometric
$a_5=\frac{1}{a^3}$
Work Step by Step
We are given the sequence $\{a_n\}$:
$$a,1,,\dfrac{1}{a},\dfrac{1}{a^2}\dots $$
Check if the sequence is geometric:
$$\begin{align*}
\dfrac{a_2}{a_1}&=\dfrac{1}{a}\\
\dfrac{a_3}{a_2}&=\dfrac{\frac{1}{a}}{1}=\dfrac{1}{a}\\
\dfrac{a_4}{a_3}&=\dfrac{\frac{1}{a^2}}{\frac{1}{a}}=\dfrac{1}{a}.
\end{align*}$$
Since the ratios between consecutive terms are constant, the sequence is geometric.
Its first term is $a_1=a$ and its common ratio $r=\frac{1}{a}$.
We calculate the fifth term:
$$a_5=a_4r=\dfrac{1}{a^2}\cdot\dfrac{1}{a}=\dfrac{1}{a^3}.$$
