What is the nth term for -2-7 -12 -17 -22?

Answer 1

There are infinitely many polynomials of order 5 that will give these as the first five numbers and any one of these could be "the" rule. 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 may think that the rule is subtract 5, and so the next number should be -27.

But the following polynomial also fits:

U(n) = (n^5 - 15*n^4 + 85*n^3 - 225*n^2 + 254*n - 108)/4 and according to that, the next number should be 0. It is possible to find a polynomial so that ANY number can be the next and that, of course, changes the rest of the sequence. But it still meets the requirements of the first 5 numbers.

The simplest solution, based on a linear equation is

U(n) = 3 - 5n