Find the missing number in the series Question: 6, 9, _, 24, 36

Concept: In a number series, first compute the differences between consecutive terms. If those differences themselves follow a clear rule — here, each difference is 3 times an increasing whole number (3×1, 3×2, 3×3, 3×4) — that rule fixes every term, including a missing one.

Application: Apply the rule to 6, 9, _, 24, 36:

1. The first difference is 9 − 6 = 3, which is 3 × 1.

2. The next difference should be 3 × 2 = 6, so the missing term is 9 + 6 = 15.

3. The following difference should be 3 × 3 = 9, giving 15 + 9 = 24 — matching the 24 already given.

4. The last difference should be 3 × 4 = 12, giving 24 + 12 = 36 — matching the 36 already given.

Cross-check: All four consecutive differences — 3, 6, 9, 12 — are exactly 3 × 1, 3 × 2, 3 × 3, 3 × 4, and the last two reproduce the terms 24 and 36 that were already given, confirming the pattern is consistent end-to-end.

Answer: 15