Chapter 8.2, Problem 3E

Solve these recurrence relations together with the initial conditions given.

a) $a_n=2a_{n-1}$ for $n\ge 1$ , $a_0=3$

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

C) $a_n=5a_{n-1}-6a_{n-2}$ for $n\ge 2$ , $a_0=1$ , $a_1=0$

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

e) $a_n=-4a_{n-1}-4a_{n-2}$ for $n\ge 2$ , $a_0=0$ , $a_1=1$

f) $a_n=4a_{n-2}$ for $n\ge 2$ , $a_0=0$ , $a_1=4$

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