I am having trouble finding initial conditions for closed sequences. Could you help me get through this problem from my textbook? Thanks!
Show that $3 · 2^n + 7 · 5^n$ is a solution to the recurrence relation, $a_{n} = 7a_{n−1} − 10a_{n−2}$. What would the initial conditions need to be for this to be the closed formula for the sequence?
The initial conditions are $a_0=3+7=10$ and $a_1=3\times2+7\times5=41$, of course.