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Any number that you choose can be the 8th term. 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 and the chosen eighth number. 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, the simplest answer, based on a polynomial of order 4, is 46259.

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Q: What is the 8th term of this pattern 3 19 99 499 2499?
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