Exercise 13.

Consider the recurrence relation \(a_n = 4a_{n-1} - 4a_{n-2}\text{.}\)

1. Find the general solution to the recurrence relation (beware the repeated root).

2. Find the solution when \(a_0 = 1\) and \(a_1 = 2\text{.}\)

3. Find the solution when \(a_0 = 1\) and \(a_1 = 8\text{.}\)