8, 12, 24, 60 — what is the next number in the series?

Concept: When consecutive terms of a series do not share a common difference or common ratio directly, compute the sequence of first differences between consecutive terms. If those differences themselves follow a recognizable pattern — often a constant ratio (a geometric progression) — extend that pattern one step further and add the result to the last given term.

Application:

1. Find the differences between consecutive terms: 12 − 8 = 4, 24 − 12 = 12, 60 − 24 = 36.

2. Compare consecutive differences: 12 ÷ 4 = 3, and 36 ÷ 12 = 3 — so each difference is 3 times the previous one, forming a geometric progression with common ratio 3.

3. Extend the pattern: the next difference is 36 × 3 = 108.

4. Add this difference to the last given term: 60 + 108 = 168.

Cross-check: the ratio between consecutive differences stays constant at 3 throughout (4 → 12 → 36 → 108), confirming the pattern holds consistently; adding 108 to 60 gives 168.