Answer
Neither
Work Step by Step
We are given the sequence $\{a_n\}$:
$$1,-\dfrac{3}{2}, 2,-\dfrac{5}{2},\dots $$
Check if the sequence is arithmetic:
$$\begin{align*}
a_2-a_1&=-\dfrac{3}{2}-1=-\dfrac{5}{2}\\
a_3-a_2&=2-\left(-\dfrac{3}{2}\right)=\dfrac{7}{2}\\
a_4-a_3&=-\dfrac{5}{2}-2=-\dfrac{9}{2}.
\end{align*}$$
Since the differences between consecutive terms are not constant, the sequence is not arithmetic.
Check if the sequence is geometric:
$$\begin{align*}
\dfrac{a_2}{a_1}&=\dfrac{-\frac{3}{2}}{1}=-\dfrac{3}{2}\\
\dfrac{a_3}{a_2}&=\dfrac{2}{-\frac{3}{2}}=-\dfrac{4}{3}\\
\dfrac{a_4}{a_3}&=\dfrac{-\frac{5}{2}}{2}=-\dfrac{5}{4}.
\end{align*}$$
Since the ratios between consecutive terms are not constant, the sequence is not geometric.
So the sequence is neither arithmetic, nor geometric.
