1.

e _n=3 e _{n ? 1} (Of course, this you can do in your head, but practice the method of the section.)

2.

d _{n+ 1}= ?2 d _n , d ₁=3

3.

In Example 1, Section 5.2, we assumed it was clear from past experience that a _n = ar ⁿ is the general solution to

However, it s worth a proof, or two, for practice.

1. Verify that a _n =ar ⁿ satisfies (15), where a=a ₀. (Thus by Theorem 1, Section 5.4, all solutions are of this form.)

2. Use the characteristic equation method of this section to prove that ar ⁿ is the general solution to (15).

4.

a _n =a _{n ? 1}+2 a _{n ?2}, a ₁=2, a ₂=3.

5.

a _n =a _{n ? 1}+ a _{n ?2}, a ₀=1, a ₁=3.

6.

a _{n+ 1}=5 a _n ?6 a _{n ?1}, a ₁= ?1, a ₂=1.

7.

a _n= ?2 a _{n ? 1} ? a _{n ?2}, a ₀=1, a ₁=2.

8.

Same as [6] except a ₁=5, a ₂ =7.

9.

Same as [7], but a ₀=1, a ₁=