How can you write an equation for 13 26 39 412?

Answer 1

There are infinitely many polynomials of order 4 that will give these as the first four numbers and any one of these could be "the" rule.

The simplest rule, based on a polynomial of order 3 is

T(n) = 60*n^3 - 360*n^2 + 673*n - 360 for n = 1, 2, 3, 4.

In order to find this polynomial you need to find the regression equation for the data set (1, 13), (2, 26), (3, 39) and (4, 412).

There are also non-polynomial solutions.