Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next?

Concept: In an alternating-operation number series, two different operations repeat in a fixed cycle (here, multiply then subtract) instead of one constant rule. Solve it by finding the operation linking each consecutive pair and confirming that the same two operations recur every cycle.

Applying the cycle term by term:

1. 14 to 28: 14 × 2 = 28.

2. 28 to 20: 28 − 8 = 20.

3. 20 to 40: 20 × 2 = 40.

4. 40 to 32: 40 − 8 = 32.

5. 32 to 64: 32 × 2 = 64.

6. Continuing the same cycle, the next step subtracts 8 from 64: 64 − 8 = 56.

Cross-check: Re-applying the rule from the first term reproduces the entire given series exactly (14, 28, 20, 40, 32, 64), confirming the multiply-by-2-then-subtract-8 cycle, so the series continues with 56.