544, 509, 474, 439, ?

Solution: 404. Each term falls by 35.

Solution: 116. Gaps 6, 12, 20, 30 grow by 6, 8, 10, so the next gap is 42.

8, 10, 23, 73, 292, 1491

Solution: 292. ×1 + 2, ×2 + 3, ×3 + 4, ×4 + 5, ×5 + 6: 73 × 4 + 5 = 297, and 297 × 5 + 6 = 1491 confirms it.

What are the common traps in Number series: missing / wrong term questions?

Early gap reuse: in 5, 8, 13, ?, 29 the gaps are 3, 5, 7, 9, so 20, not 18 or 22. Sign slips: alternating series (+11, −13, +17, −19 …) are usually spoiled by one dropped minus. Decimal multipliers: 16, 8, 8, 12, 24, ? multiplies by 0.5, 1, 1.5, 2, 2.5: the next multiplier is 2.5, not 3. Wrong-term offset: in 56, 72, 90, 110, 132, 139 the gaps 16, 18, 20, 22 point to 156; the wrong term is 139, the last one, not 132.

Start here · the first lesson of Number series: missing / wrong term

Number series: missing / wrong term

Series (number / letter / alphanumeric) · for IPMAT Indore, IPMAT Rohtak and JIPMAT

The idea

A number series follows one rule from term to term: a constant or growing gap, a multiplier with a small adjustment, powers (squares, cubes, factorials, primes), or two rules woven together. IPMAT Rohtak asks 2–5 such questions a year and JIPMAT 2–3, as "find the missing term", "find the wrong term" or a match-the-lists set of four short series.

Textbook vs exam method

Textbook method

Compute successive differences; if they are constant the series is arithmetic; if the differences themselves form a pattern, continue that pattern; otherwise test ratios between consecutive terms and finally compare terms with known sequences (squares, cubes, factorials, primes).

Exam method

Gaps first. Write the differences under the terms. Constant → add it. Growing by a constant → second differences (JIPMAT 2023: 2, 12, 30, 56, 90: gaps 10, 18, 26, 34, +8 each → 132).
Big growth → multiply. If terms roughly triple or quadruple, test term × k ± c (Rohtak 2020: 12, 38, 116, 350, 1052 = ×3 + 2 → 3158).
Recognise landmarks. 24, 120, 720 are factorials; 121, 169, 289 are prime squares; 8, 27, 125, 343 are cubes of primes. The series is then that sequence plus a small counter.
No sense? Split. Read alternate terms (Rohtak 2019: 2, 7, 10, 22, 18, 37, 26, ? → 7, 22, 37, 52).
Wrong term. Find the rule from the agreeing terms; the one term off the chain is the answer, and the following term should fit again once the error is corrected.
Match-the-lists. Solve the easiest series first and eliminate options after each one; two solved series usually leave a single option.