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What are the list 39 12 15 18?
The list comprises the first 4 numbers of the sequence: Un = -5n3 + 45n2 - 127n + 126 for n = 1, 2, 3, ...
What is the tenth number in this sequence5-10-25-40?
Given any number it is easy to find a rule based on a polynomial of order 4 such that the first four numbers are as listed in the question and the tenth is the given number. That is, it is easy to find a rule so that any number can be the "tenth" in the sequence.For example:Un = (15n4 - 190n3 + 885n2 - 1430n + 840)/24 would give U10 = 1460orUn = (15n4 - 170n3 + 705n2 - 1090n + 600)/12 would give U10 = 3350and so on.The appropriate polynomial of order 3 isUn = (-5n3 + 45n2 - 85n + 60)/3 according to which, U10 = 430.
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