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I am assuming that the question is about a sequence, not a series. The two are related but are not the same.
Given any number it is easy to find a rule based on a polynomial of order 6 such that the first six numbers are as listed in the question and the next is the given number. There are also non-polynomial solutions.
The simplest polynomial of order 5 is
Un = (-87n5 + 1540n4 - 9965n3 + 28460n2 - 34228n + 14880)/120 where n = 1, 2, 3, ...
Accordingly, the next number is -107.
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