What is the original sequence for 15 25 10?

Answer 1

There are infinitely polynomials of order 3 that will give these as the first three numbers and any one of these could be "the" rule. 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.

Here, the simplest solution, based on a polynomial of order 2, is

t(n) = 2.5* (-5*n^2 + 19*n - 8) for n = 1, 2, 3, ...