The sequence $a_1, a_2, a_3, ...$ satisfies that $a_1 = 3$, $a_2 = -1$, $a_na_{n-2} +a_{n-1} = 2$ for all $n \ge 3$. Calculate $a_1 + a_2+ ... + a_{99}$.
Source: 2006 Cuba MO 2.7
Tags: algebra, recurrence relation, Recurrence
The sequence $a_1, a_2, a_3, ...$ satisfies that $a_1 = 3$, $a_2 = -1$, $a_na_{n-2} +a_{n-1} = 2$ for all $n \ge 3$. Calculate $a_1 + a_2+ ... + a_{99}$.