Question

what is the next number sequence for 0,10,24,56,112,190

Answer 1

Take a look at the Newton's Method of Divided Differences. The polynomial of lowest degree which fits these data points is

0 + 10(x) + 2(x)(x-1) + (7/3)(x)(x-1)(x-2) + (-1/3)(x)(x-1)(x-2)(x-3)

The next values are 280 364

Answer 2

280

Answer 3

why 280