Chapter 12 Sequences and Series - 12.5 Use Recursive Rules with Sequences and Functions - 12.5 Exercises - Skill Practice - Page 831: 34

$a_n=a_{n-2}^2+a_{n-1}$

We study the terms of the given sequence and notice the pattern: $$\begin{align*} a_1&=3\\ a_2&=8\\ a_3&=3^2+8=17\\ a_4&=8^2+17=81\\ a_5&=17^2+81=370. \end{align*}$$ The recursive rule is: $$a_n=a_{n-2}^2+a_{n-1}.$$