Determining the fourth term of $c_k = kc_{k-1}^2$

Question

What is the fourth term of the following recursively defined sequence?

$c_k = kc_{k-1}^2$ for integers $k \ge 1$ and $c_0 = 1$.

The possible answers are $12$ and $20$. I am not sure which one it is and how to decide this.

Answer 1

You mean $c_k = k(c_{k-1})^2$?

$c_0 = 1$

$c_1 = 1 \times c_0^2 = 1 \times 1^2 = 1$

$c_2 = 2 \times c_1^2 = 2 \times 1^2 = 2$

$c_3 = 3 \times c_2^2 = 3 \times 2^2 = 12$

$c_4 = 4 \times c_3^2 = 4 \times 12^2 = 576$

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