3, -6, 12, 4, 20

The odd terms go

 3, add 9, get 12, add 8, get 20

We added 9, then we added 8. which is 1 less than 9.

So we might guess that the even terms add 1 less each time, too

So the even terms go

-6, add 10, get 4, so we'd add 1 less or 9, and get 13.

So I'd pick 13, assuming that the even terms add 1 less each time
like the odd terms do.  That's as logical as any other guess as to
what they do.

Edwin