What is the next number in the series: 8, 16, 24, 36, 48, ?

Concept: This series is built by alternating between two rules for consecutive integers n: an odd step gives n2 − 1, and the following even step gives n2 exactly. The value of n increases by 1 with every term.

1. n = 3: 32 − 1 = 9 − 1 = 8

2. n = 4: 42 = 16

3. n = 5: 52 − 1 = 25 − 1 = 24

4. n = 6: 62 = 36

5. n = 7: 72 − 1 = 49 − 1 = 48

6. n = 8: 82 = 64 → this is the next term

Cross-check: The gaps between the five known terms are 8, 8, 12, 12 — repeating in equal pairs and growing by 4 every two terms. Continuing that pattern, the next gap must also repeat within its pair at 16, giving 48 + 16 = 64 — confirming the same result independently.