Solution to the following recurrence relation and initial condition? With the initial condition being $a_0$ = 3, and the relation being $a_n = 2a_{n - 1}$, what would the solution be? Any help would be greatly appreciated.
Try to calculate $a_1$. You'll see that $a_1=2\times3$. Then $a_2=2a_1=2\times2\times3=2^2\times3$. 

Conjecture that $a_n=3.2^n$ for all $n\ge 0$.

Prove by induction.