Next number in sequence 20 25 32?

Answer 1

Any number that you choose can be the next number. It is easy to find a rule based on a polynomial of order 3 such that the first three numbers are as listed in the question followed by the chosen next 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.

For example,

You want the next number to be 1? Then U(n) = (-20n^3 + 123n^2 - 214n + 171)/3

You want the next number to be 2? Then U(n) = (-13n^3 + 80n^2 - 139n + 112)/2You want the next number to be 11? Then U(n) = -7n^3 + 40n^2 - 70n + 56

You want the next number to be 101? Then U(n) = 10n^3 - 59n^2 + 112n - 43