What is the next number in the series? 1, 2, 4, 7, 11, 16, __

Subtract each number from the next. This is the series of "first differences" and it often gives a clue as to the rule used to generate the series. In this series, first differences are
  1, 2, 3, 4, 5
We speculate that the next first difference will be 6, so the next term is
  16 + 6 = 22

22