What is the number after 3 6 12 6 12 24 18?

Answer 1

It can be any number you like. It is alwayspossible to find a polynomial of degree 7 that will fit all the given values as well as the additional point.

You can fit the following rule:

Un = (9n6 - 235n5 + 2395n4 - 12025n3 + 30836n2 - 37300n + 16560)/80 for n = 1, 2, 3, ... and, according to that position-to-value rule, the next number is 45.

This may not be the rule you want, but it is a perfectly valid rule.