Solution:
This is a simple addition series with a random number, 8, interpolated as every other number. In the series, 6 is added to each number except 8, to arrive at the next number.

Workspace

12.

Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?

Solution: In this alternating repetition series, the random number 21 is interpolated every other number into an otherwise simple addition series that increases by 2, beginning with the number 9.

Workspace

15.

Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?