TNPSC Group IV · Bite-size lessons

Number Series

About 6 min · Aptitude and Mental Ability Test · English

Time worked out from the lesson's 368 words at 150 words a minute, plus a minute for each question.

Number series is a listed topic in TNPSC Group IV's Aptitude and Mental Ability section. Questions typically present a sequence of numbers following a hidden pattern, and you must identify the next term, find a missing term, or spot the wrong term that breaks the pattern.

Key ideas

• Arithmetic Progression (AP): Each term increases or decreases by a constant value. Example: 3, 7, 11, 15, 19 (common difference = 4).
• Geometric Progression (GP): Each term is multiplied or divided by a constant value. Example: 2, 6, 18, 54, 162 (common ratio = 3).
• Difference of Differences: When first differences aren't constant, check second-level differences. If 2, 5, 10, 17, 26... has differences 3, 5, 7, 9 (increasing by 2), the pattern is in the second level.
• Square and Cube Series: Terms are perfect squares (1, 4, 9, 16, 25) or cubes (1, 8, 27, 64, 125), or derived from them (n² + 1, n³ – n).
• Alternating Series: Two separate patterns interleaved. In 2, 5, 4, 10, 6, 15, odd positions (2, 4, 6) and even positions (5, 10, 15) follow different rules.

Watch out for

• Assuming only one pattern exists → Always verify your pattern works for ALL given terms, not just the first few. A pattern that fits three terms may fail on the fourth.
• Missing alternating series → When differences seem random, check if odd-positioned and even-positioned terms form separate series. Split and analyze independently.
• Confusing n² and 2n patterns → The series 2, 4, 8, 16 is GP (×2), not squares. The series 1, 4, 9, 16 is n². Calculate carefully before concluding.

Quick reference

• First step always: Calculate differences between consecutive terms.
• Second-level check: If differences vary, find differences of those differences.
• Memorize: Squares up to 20² (400), cubes up to 10³ (1000), primes up to 50.
• Alternating series: Separate odd and even positions, solve as two series.
• Wrong term: Find the pattern, calculate correct values, identify the mismatch.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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