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How do you determine the rule of a sequence? - Answers

It is impossible. Given any set of n numbers, it is easy to find infinitely many polynomials of order n that can be used as a rule for those numbers. In addition, there are non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one. The best that you can do is Occam's test: go for the simplest solution. For example, what is the rule for the sequence 10, 20, 30, 40, 50? Is it t(n) = 10*n? Why not t(n) = (n^5 - 15*n^4 + 85*n^3 - 225*n^2 + 334*n - 120)/6 ? For n = 1 , 2, 3, 4, 5 they give the same result: the sequence for which you are seeking a rule. Mathematically, both answers are equally valid.



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How do you determine the rule of a sequence? - Answers

https://math.answers.com/math-and-arithmetic/How_do_you_determine_the_rule_of_a_sequence

It is impossible. Given any set of n numbers, it is easy to find infinitely many polynomials of order n that can be used as a rule for those numbers. In addition, there are non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one. The best that you can do is Occam's test: go for the simplest solution. For example, what is the rule for the sequence 10, 20, 30, 40, 50? Is it t(n) = 10*n? Why not t(n) = (n^5 - 15*n^4 + 85*n^3 - 225*n^2 + 334*n - 120)/6 ? For n = 1 , 2, 3, 4, 5 they give the same result: the sequence for which you are seeking a rule. Mathematically, both answers are equally valid.



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https://math.answers.com/math-and-arithmetic/How_do_you_determine_the_rule_of_a_sequence

How do you determine the rule of a sequence? - Answers

It is impossible. Given any set of n numbers, it is easy to find infinitely many polynomials of order n that can be used as a rule for those numbers. In addition, there are non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one. The best that you can do is Occam's test: go for the simplest solution. For example, what is the rule for the sequence 10, 20, 30, 40, 50? Is it t(n) = 10*n? Why not t(n) = (n^5 - 15*n^4 + 85*n^3 - 225*n^2 + 334*n - 120)/6 ? For n = 1 , 2, 3, 4, 5 they give the same result: the sequence for which you are seeking a rule. Mathematically, both answers are equally valid.

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      It is impossible. Given any set of n numbers, it is easy to find infinitely many polynomials of order n that can be used as a rule for those numbers. In addition, there are non-polynomial solutions. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one. The best that you can do is Occam's test: go for the simplest solution. For example, what is the rule for the sequence 10, 20, 30, 40, 50? Is it t(n) = 10*n? Why not t(n) = (n^5 - 15*n^4 + 85*n^3 - 225*n^2 + 334*n - 120)/6 ? For n = 1 , 2, 3, 4, 5 they give the same result: the sequence for which you are seeking a rule. Mathematically, both answers are equally valid.

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