Finding a recurrence Relation

In summary, we are looking for a simple closed formula for the ordinary generating function of a sequence given by a_{n} = 6 * 5^n - 5 * 3^n. The question is how to find the recurrence relation for this sequence. However, instead of finding the recurrence relation, it may be easier to view this sequence as a combination of two geometric sequences and find the generating function for each. Adding the two generating functions together will give us the desired generating function for the given sequence.
  • #1
Punkyc7
420
0
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.
 
Physics news on Phys.org
  • #2
Punkyc7 said:
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?
 

What is a recurrence relation?

A recurrence relation is a mathematical equation that defines a sequence or series by expressing each term in terms of the previous one or ones.

Why is finding a recurrence relation important?

Finding a recurrence relation is important because it allows us to describe and understand a sequence or series in a concise and efficient way. It can also help us make predictions about future terms in the sequence and solve more complex mathematical problems.

How do you find a recurrence relation?

To find a recurrence relation, you need to analyze the given sequence or series and look for a pattern among the terms. This usually involves finding a relationship between each term and the previous one, which can then be expressed in a mathematical equation.

What are some common methods for finding a recurrence relation?

There are several common methods for finding a recurrence relation, including the substitution method, the iteration method, and the generating function method. Each method involves a different approach to identifying the pattern and writing a corresponding recurrence relation.

How can a recurrence relation be used in real-world applications?

A recurrence relation can be used in various real-world applications, such as in computer science, physics, and finance. For example, in computer algorithms, recurrence relations can be used to optimize the time and space complexity of a program. In physics, they can be used to describe the behavior of a system over time. In finance, they can be used to model the growth of investments or the repayment of loans.

Similar threads

  • Calculus and Beyond Homework Help
Replies
8
Views
938
  • Calculus and Beyond Homework Help
Replies
5
Views
436
  • Calculus and Beyond Homework Help
Replies
3
Views
515
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
92
  • Calculus and Beyond Homework Help
Replies
1
Views
908
  • Calculus and Beyond Homework Help
Replies
7
Views
978
  • Calculus and Beyond Homework Help
Replies
6
Views
859
  • Calculus and Beyond Homework Help
Replies
1
Views
664
Back
Top