Question 75
Let the sequence $\{a_n\}$ be defined by $a_1 = 1$, $a_2 = 2$, $a_{n+1} = \frac{a_n^2 + (-1)^n}{a_{n-1}}$ $(n = 2, 3, \dots)$.
Prove that the sum of squares of any two adjacent terms of the sequence is also in the sequence.
Prove that the sum of squares of any two adjacent terms of the sequence is also in the sequence.