Question 8
A sequence $(a_n)$ satisfies $a_1 = 2$, $a_2 = 3$, $a_3 = 5$ and $a_n = a_{n-1}^2$ for any $n \ge 4$. A sequence $(b_n)$ satisfies $b_1 = 2$, $b_2 = 3$, $b_3 = 5$ and $b_n = b_{n-1} \cdot b_{n-2} \cdot b_{n-3}^2$ for any $n \ge 4$. A sequence $(c_n)$ satisfies $c_1 = 2$, $c_2 = 3$, $c_3 = 5$ and $c_n = c_1 \cdot c_2 \cdots c_{n-1}$ for any $n \ge 4$. Order the numbers $a_{1000}$, $b_{1000}$ and $c_{1000}$ by size.