Answer
Common ratio: $2i$
Work Step by Step
We are given the sequence $\{a_n\}$:
$$3,6i,-12,-24i,\dots$$
We calculate the ratio of consecutive terms:
$$\begin{align*}
\dfrac{a_2}{a_1}&=\dfrac{6i}{3}=2i\\
\dfrac{a_3}{a_2}&=\dfrac{-12}{6i}=2i\\
\dfrac{a_4}{a_3}&=\dfrac{-24i}{-12}=2i.
\end{align*}$$
As all ratios are constant, the sequence is geometric. The common ratio is $2i$.
