What number should replace the question mark in the series given below? 12, 12, 24, 72, 288, ?, 8640

The missing number is 1440.

Each term is the previous term multiplied by 1, 2, 3, 4, ... in turn.

12 x 1 = 12, 12 x 2 = 24, 24 x 3 = 72, 72 x 4 = 288.

The next multiplier is 5, so 288 x 5 = 1440.

Check: 1440 x 6 = 8640 matches the last term.

Method: increasing-integer multiplier series.