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Finding a recurrence Relation

  • Thread starter Punkyc7
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  • #1
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Find a simple closed formula for the ordinary generating function of the sequence given by


{a[itex]_{n}[/itex]]}n>=0 when a[itex]_{n}[/itex] is given by


a[itex]_{n}[/itex] = 6 * 5^n - 5 * 3^n.


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


I don't know were to start.
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
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Find a simple closed formula for the ordinary generating function of the sequence given by


{a[itex]_{n}[/itex]]}n>=0 when a[itex]_{n}[/itex] is given by


a[itex]_{n}[/itex] = 6 * 5^n - 5 * 3^n.


My question is how do you find the recurrence relation a[itex]_{n}[/itex] = 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?
 

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