Chapter 5.8, Problem 8ES

In each of 8—10: (a) suppose a sequence of the form $1,t,t^2,t^3,\mathrm{...},t^n\mathrm{...}$ where $t\ne 0$ , satisfies the given recurrence relation (but not necessarily the initial conditions), and find all possible values of t: (b) suppose a sequence satisfies the given initial conditions as well as the recurrence relation, and find an explicit formula for the sequence.

8. $a_k=2a_{k-1}+3a_{k-2}$ , for every integer $k\ge 2$ $a_0=1,a_1=2$