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tgt
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How do you find a recurrence relation from a given problem?
tgt said:I've got a series of numbers starting with n=1 going up to n=7. I am told there exists a recurrence relation. Is that enough data to find this relationship?
rock.freak667 said:as in your series of numbers i; 1,2,3,4,5,6,7?
tgt said:no. The series I'm told to find a recurrence relation for has the first 7 numbers given to me. I know have to find a recurrence relation for these numbers.
cristo said:What you will need to do is to spot a pattern with the numbers. You should post your specific question in the homework forums, and show us what you have done towards answering the problem. Such a cryptic conversation as this will not help anyone!
A recurrence relation is a mathematical equation that defines a sequence in terms of its previous terms. It is a way to describe a pattern that repeats itself.
Finding a recurrence relation allows us to predict the values of a sequence without having to explicitly list out every term. This can save time and effort in solving complex problems.
To find a recurrence relation, you need to analyze the given sequence and look for a pattern in the values. This can involve using algebraic manipulation, substitution, or other techniques depending on the type of sequence.
Not all sequences can be described by a recurrence relation. Some may follow a random pattern or involve multiple variables that make it difficult to find a simple equation. However, many common sequences such as arithmetic, geometric, and factorial sequences can be described by recurrence relations.
One way to check the validity of a recurrence relation is by comparing its predicted values to the actual values of the sequence. If they match, then the recurrence relation is likely correct. Additionally, you can also check if the relation follows the given initial conditions and if it produces the desired pattern in the sequence.