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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 = 1460

or

Un = (15n4 - 170n3 + 705n2 - 1090n + 600)/12 would give U10 = 3350

and so on.

The appropriate polynomial of order 3 is

Un = (-5n3 + 45n2 - 85n + 60)/3 according to which, U10 = 430.

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11y ago

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