Recurrence problem for $a_5$ Assume that the sequence $\{a_0,a_1,a_2,\ldots\}$ satisﬁes the recurrence $a_{n+1} = a_n + 2a_{n−1}$. We know that $a_0 = 4$ and $a_2 = 13$. What is $a_5$?

Rearranging the recurrence relation gives $a_n = a_{n+1} - 2a_{n-1}$, so that $a_1 = 13 - 2 \cdot 4 = 5$. Now that we know $a_0,a_1$ and $a_2$ you are good to go by simply applying the recursion repeatedly until you get to the fifth term. 
