Question

what is the closed form definition for 4, -12, 36, -108?

Answer 1

we see that

$\begin{gathered} \frac{-12}{4}=-3 \\ \frac{36}{-12}=-3 \\ \frac{-108}{36}=-3 \end{gathered}$

Then, we have a geometric sequence, and each time we need to muliply by -3 starting from 4, so the closed-form is

$t(n)=4(-3)^{n-1}$

so, the answer is the second one.