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Any number that you choose can be the 100th or nth number. It is easy to find a rule based on a polynomial of order 7 such that the first seven numbers are as listed in the question followed by the chosen next number in the 100th place. 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.

However, the simplest solution here is

t(n) = 2n + 3 for n = 1, 2, 3, ...

and so t(100) = 203.

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10y ago

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