1228561203601170

The next number in the sequence is 4296.

Explanation:

The pattern of the sequence is not immediately obvious, so we need to look for a pattern in the differences between the terms.

The first differences are:

28 - 12 = 16 56 - 28 = 28 120 - 56 = 64 360 - 120 = 240 1170 - 360 = 810

The second differences are:

28 - 16 = 12 64 - 28 = 36 240 - 64 = 176 810 - 240 = 570

The third differences are all the same:

12, 36, 176, 570

This tells us that the sequence is a cubic (third-degree) polynomial. We can use the formula for a cubic polynomial to find the next term:

an = an-1 + dn-1 + (3/2)dn-2 + (1/2)dn-3

where: an = the next term an-1 = the last term dn-1 = the last first difference dn-2 = the last second difference dn-3 = the last third difference

Plugging in the values we know:

an = 1170 + 810 + (3/2)(240) + (1/2)(64) an = 4296

Therefore, the next number in the sequence is 4296.