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Any three numbers that you choose can be the next number. It is easy to find a rule based on a polynomial of order 6 such that the first four numbers are as listed in the question followed by the chosen three numbers. 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. Having said that, based on the simplest rule, the next three are 2, 7 and 12.

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Q: What are the next three terms of the arithmetic sequence -18 -13 -8 -3?
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