Answer
Answer $A$: $1,4,4,16$
Work Step by Step
We are given the recursive sequence:
$$\begin{cases}
a_1=1\\
a_2=4\\
a_n=a_{n-1}\cdot a_{n-2}.
\end{cases}$$
The first two terms of the sequence are given. We calculate $a_3$ and $a_4$ using the recursive formula:
$$\begin{align*}
a_3&=a_2\cdot a_1=4\cdot 1=4\\
a_4&=a_3\cdot a_2=4\cdot 4=16.
\end{align*}$$
The correct answer is Answer $A$.
