What are the next two numbers 12 17 22 27?

Answer 1

Any two numbers that you choose can be next. It is easy to find a rule based on a polynomial of order 5 such that the first four 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, U(n) = (-4*x^4 + 40*x^3 - 140*x^2 + 215*x - 75)/3 gives the next number as 0,U(n) = (-31*x^4 + 310*x^3 - 1085*x^2 + 1670*x - 576)/24 gives the next number as 1, and so on.The simplest rue, based on a linear expression, gives U(5) = 32 and U(6) = 37.

Answer 2

They are: 32 and 37 because they are increasing by increments of 5.