Help with linear homogeneous recurrence relations

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Homework Help Overview

The problem involves determining the order of a linear homogeneous recurrence relation with constant coefficients, specifically for the relation An = 2An-1. The original poster expresses uncertainty about how to approach the problem.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the definition of "order" in the context of recurrence relations and question the original poster's formulation of the problem. There is an exploration of the implications of different interpretations of the recurrence relation.

Discussion Status

The discussion is ongoing, with participants providing clarifications and questioning assumptions. Some guidance has been offered regarding the definition of order, but there is no explicit consensus on the interpretation of the recurrence relation or its order.

Contextual Notes

There is a noted distinction between the terms "A" and "a" in the recurrence relation, which may affect the understanding of the problem. Additionally, the original poster's formulation includes potential confusion regarding the presence of additional terms in the equation.

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Homework Statement


Here's my problem - Give the order of linear homogeneous recurrence relations with constant coefficients for: An = 2na(n-1)



The Attempt at a Solution

I have no idea on how to start this problem - Any help would be greatly appreciated.
 
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First, I think you mean An= 2An-1. Be careful to distinguish between "A" and "a"!

Notice that this problem does not (yet) ask you to solve the equation! It just asks that you state its order. Do you know the definition of "order" of a recurrence relation? I suspect the way to "start this problem" is to look up "order"!
 
=2(2An-1 + 1) + 1
=2^2An-1 + 2 + 1

Is this right?
 
The order is just the number of "previous" terms, in which case the order is 2
 
No, in the recursion An= 2An-1, An depends on the value of A one place before it. The order is 1.

As for
=2(2An-1 + 1) + 1
=2^2An-1 + 2 + 1

I can't tell whether it is correct or not because you haven't told me what it is supposed to equal!

Once again, is this intended to be An= 2Sn-1? If so, I cannot see where you are getting the "+1" terms from.

Suppose A0= 1. What is A1? A2?
 

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