Look at this series: 14, 28, 20, 40, 32, 64, 56... What number should come next?

Concept: An alternating (zig-zag) number series applies two different operations one after another in a repeating pattern (Operation 1, Operation 2, Operation 1, Operation 2, ...) instead of a single fixed rule from term to term. To find the next term, identify the operation pair linking consecutive terms and confirm it holds consistently across the whole series before extending it.

1. 14 to 28: multiply by 2 (14 × 2 = 28).

2. 28 to 20: subtract 8 (28 − 8 = 20).

3. 20 to 40: multiply by 2 (20 × 2 = 40).

4. 40 to 32: subtract 8 (40 − 8 = 32).

5. 32 to 64: multiply by 2 (32 × 2 = 64).

6. 64 to 56: subtract 8 (64 − 8 = 56).

7. 56 to the next term: the pattern returns to the multiply-by-2 step, so 56 × 2 = 112.

Cross-check: Grouping the series into pairs (14, 28), (20, 40), (32, 64) shows each pair's second term is exactly double the first, confirming the recurring ×2 step, while each gap between pairs (28 to 20, 40 to 32, 64 to 56) is a consistent −8. Since the series has just completed a −8 step, the next step must be the ×2 step again, giving 112.