How to Derive a Recurrence Relation for a Combined Geometric Sequence?

[Punkyc7]

Find a simple closed formula for the ordinary generating function of the sequence given by


{a$_{n}$]}n>=0 when a$_{n}$ is given by


a$_{n}$ = 6 * 5^n - 5 * 3^n.


My question is how do you find the recurrence relation a$_{n}$ = 6 * 5^n - 5 * 3^n.


I don't know were to start.

 

[gabbagabbahey]

Find a simple closed formula for the ordinary generating function of the sequence given by


{a$_{n}$]}n>=0 when a$_{n}$ is given by


a$_{n}$ = 6 * 5^n - 5 * 3^n.


My question is how do you find the recurrence relation a$_{n}$ = 6 * 5^n - 5 * 3^n.


I don't know were to start.

Why bother with finding a recurrence relation? Your sequence looks like a combination of two geometric sequences. What is the the generating function for each one? What do you get when you add the two generating functions together?