3, -6, 12, 4, 20

Question

What is the next number in the sequence

Answer 1

Again a reasonable approach is that there are actually 2 sequences involved.

The 1st and 3rd first differences are -9 and -8 suggesting that the 5th one will be -7 which would make the next term 23. The 2nd and 4th first differences are 18 and 16, suggesting that the term after 23 would be 37.

There may be other possible solutions, but the one I have suggested satisfied the limited data available.