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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 with the chosen number in nth position. 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, in this particular case, it is very likely that the sequence is that of the odd numbers.

The first term in the sequence, a = 1

The common difference, d = 2. This is the difference between each term and the one preceding it.

Then t(n) = a + (n-1)*d

= 1 + (n - 1)*2 = 1 + 2*n - 2 = 2*n -1

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