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Anynumber can be the next number - or, by extension, the tenth number in the sequence. 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 next is any number of your choice. There are also 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 simplest solution, based on a polynomial of order 3 is

t(n) = (-n^3 + 7*n^2 - 44*n + 52)/2 for n = 1 , 2, 3, ...

In that case, t(10) = -344.

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