Chapter 8.2, Problem 4E

Solve these recurrence relations together with the initial conditions given.

a) $a_n=a_{n-1}+6a_{n-2}$ for $n\ge 2$ , $a_0=3$ , $a_1=6$b) $a_n=7a_{n-1}-10a_{n-2}$ for $n\ge 2$ , $a_0=2$ , $a_1=1$

c) $a_n=6a_{n-1}-8a_{n-2}$ for $n\ge 2$ , $a_0=4$ , $a_1=10$

d) $a_n=2a_{n-1}-a_{n-2}$ for $n\ge 2$ , $a_0=4$ , $a_1=1$

e) $a_n=a_{n-2}$ for $n\ge 2$ , $a_0=5$ , $a_1=-1$

f) $a_n=-6a_{n-1}-9a_{n-2}$ for $n\ge 2$ , $a_0=3$ , $a_1=-3$

g) $a_{n+2}=-4a_{n+1}+5a_n$ for $n\ge 0$ , $a_0=2$ , $a_1=8$