Find the missing number in the following number series: 22.5, ______, 26.5,…

CONCEPT: In this type of number series, the gaps between consecutive terms don't stay constant — they change by a fixed amount from one gap to the next (a second-order arithmetic pattern). Once enough consecutive gaps are known to reveal that fixed step, the sequence of gaps can be extended backward or forward to recover any missing term.

Application to this series:

1. List the terms with the blank in place: 22.5, ?, 26.5, 30, 34.5.

2. Compute the two fully known consecutive gaps: 30 − 26.5 = 3.5 and 34.5 − 30 = 4.5.

3. Find the fixed step between successive gaps: 4.5 − 3.5 = 1.0 — each gap in the series is exactly 1.0 more than the one before it.

4. Work this step backward to get the gap just before the blank: 3.5 − 1.0 = 2.5, and the gap into the blank: 2.5 − 1.0 = 1.5.

5. Add that gap to the first term: 22.5 + 1.5 = 24.0.

Cross-check: Rebuilding the full series with 24 in place gives gaps 1.5, 2.5, 3.5, 4.5 — each exactly 1.0 more than the last, and the last two match the given terms 30 and 34.5 exactly. This confirms 24 is correct.

Therefore, the missing number is 24.