It is possible for any number to be the next number since it is always possible (and quite easy) to find a polynomial of order 5 that will fit the above numbers and the selected extra one. And that is without considering non-polynomial functions!
The only polynomial of order 4, though, is
Un = (103n4 - 1242n3 + 5201n2 - 8670n + 4680)/24 for n = 1, 2, 3, ... and occording to that, the next number in the sequence is 213.
20
3, -6, 12, 4, 20, ?
56
10 The sequence is given by xn = 60/n
The given pattern appears to alternate between two sequences: one sequence that doubles the previous number (3 to 6 to 12) and another that adds 1 to the previous number (4 to 20). Following this pattern, after 20, the next number in the doubling sequence would be 24, as it continues from 12. Thus, the next number in the pattern is 24.
25 is the next number that appears in that sequence.
20
20
3, -6, 12, 4, 20, ?
56
next in the sequence: 10,20,30,20
10 The sequence is given by xn = 60/n
16
Those are the factors of the number 60, in descending order. The next factor is 10.
22
The next number in the sequence will be 56.
20