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Any number that you choose can be the nth 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 followed by the chosen number as the nth. 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.

For example, if you want the 7th number to be 2, use

U(n) = (n^5 - 15*n^4 + 85*n^3 - 225*n^2 + 154*n + 120)/120 for n = 1, 2, 3, ...

If you want the 8th number to be 6, then use

U(n) = (n^5 - 15*n^4 + 85*n^3 - 225*n^2 -6*n + 440)/140 for n = 1, 2, 3 ...

The simplest solution, though, based on a polynomial of order to is

U(n) = 4 - 2*n

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Q: What is the nth term of 2 0 -2 -4 -6?
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