What should come at the place of question mark? 3, 8, 15, 24, 35, ?

Correct — A.
Rule: n² − 1 for n = 2, 3, 4 …

2² − 1 = 3, 3² − 1 = 8, 4² − 1 = 15
5² − 1 = 24, 6² − 1 = 35

Next is 7² − 1 = 49 − 1 = 48 → option (a).

Check: the differences 5, 7, 9, 11 rise by 2, so the next is 13, and 35 + 13 = 48.

Why the others are wrong

• (b)
  46 — 46 adds 11 again, repeating the last difference. The differences 5, 7, 9, 11 rise by 2, so the next is 13 and 35 + 13 = 48.
• (c)
  47 — 47 adds 12. The differences are consecutive odd numbers, 5, 7, 9, 11, so the next is 13, not 12.
• (d)
  49 — 49 is 7² itself. Every term is a square minus 1 (35 = 36 − 1), so the next is 49 − 1 = 48.

Numbers just below perfect squares are worth spotting on sight: 3, 8, 15, 24, 35 are 4 − 1, 9 − 1, 16 − 1, 25 − 1, 36 − 1.

The same series reads as n(n + 2): 1 × 3, 2 × 4, 3 × 5, 4 × 6, 5 × 7, giving 6 × 8 = 48. Both readings land on the same term, because n² − 1 = (n − 1)(n + 1).

Key facts

• The terms are n² − 1 for n = 2 to 6, so the next is 7² − 1 = 48.
• n² − 1 = (n − 1)(n + 1), so the terms are also 1 × 3, 2 × 4, 3 × 5 and so on.
• Consecutive squares differ by consecutive odd numbers, which is why the differences here run 5, 7, 9, 11.

Common traps

• Picking 49 because 7² comes next, and forgetting the − 1 that every term carries.
• Repeating the last difference (35 + 11 = 46) instead of letting it grow by 2.

No directly related past PYQ was found.