What is next number in series 3 -6 12 4 20?

Answer 1

Given ANY number whatsoever, it is easy to find a polynomial of order 5 that will generate the above five numbers and your sixth as the first six. So the simplest answer to the question is what would you like it to be - and I can find you the rule that works for it.

However, the simplest polynomial of order 4 that fits the above numbers is

Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, 3, ...

and accordingly, the next number is 213.