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Given any number it is easy to find a rule based on a polynomial of order 5 such that the first five numbers are as listed in the question and the nth is the given number. There are also non-polynomial solutions.
The simplest polynomial of smaller order is:
Un = (n2 + n + 4)/2 for n = 1, 2, 3, ...
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Earn +20 ptsQ: What is the nth term for 3 5 8 12 17?
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