Answer
$$a_1=6 \hspace{5mm} a_{k+1}=\frac{1}{3}a_k^2$$
$a_1=6$
$a_2=12$
$a_3=48$
$a_4=768$
$a_5=196608$
Work Step by Step
The successive terms are found my squaring the previous term and dividing it by 3. The first term is given to us $a_1=6$. We can find the second term by squaring the number our first term and dividing it by 3
$$a_2=\frac{1}{3}a_1^2=\frac{1}{3}6^2=\frac{1}{3}\times 36 = 12$$.
We can repeat the exact same process to find the third term
$$a_3=\frac{1}{3}a_2^2=\frac{1}{3}12^2=\frac{1}{3}\times 144 = 48$$,
for our fourth
$$a_4=\frac{1}{3}a_3^2=\frac{1}{3}48^2=\frac{1}{3}\times 2304 = 768$$,
and finally for our fifth
$$a_5=\frac{1}{3}a_4^2=\frac{1}{3}768^2=\frac{1}{3}\times 589824 = 196608$$.
