Find the missing term in the following series : 0, 3, 8, ?, 24, 35

Concept: In a number-series question, first find the differences between consecutive terms that are already known. If those differences themselves form a simple pattern (a constant value, an arithmetic progression, or squares), extend that pattern to fill the missing term(s).

1. List the terms by position: T1 = 0, T2 = 3, T3 = 8, T4 = ?, T5 = 24, T6 = 35.

2. Compute the differences that can already be found: T2 − T1 = 3, T3 − T2 = 5, and T6 − T5 = 11.

3. The known differences 3 and 5 differ by 2, matching the step size of a consecutive-odd-number sequence; extending that sequence to five terms gives 3, 5, 7, 9, 11, whose last value (11) equals the known T6 − T5 = 11, confirming the full difference sequence is 3, 5, 7, 9, 11.

4. Use the missing differences to find T4: T4 = T3 + 7 = 8 + 7 = 15; check forward, T5 = T4 + 9 = 15 + 9 = 24, which matches the given fifth term.

Cross-check: every term also fits the formula Tn = n2 − 1 — 12 − 1 = 0, 22 − 1 = 3, 32 − 1 = 8, 42 − 1 = 15, 52 − 1 = 24, 62 − 1 = 35 — an independent method that reproduces all five given terms and confirms the missing term.

So the missing term is 15.