HSSC CET · Bite-size lessons

Series Completion

About 6 min · Reasoning Ability · English

Time worked out from the lesson's 321 words at 150 words a minute, plus a minute for each question.

Series Completion is a core reasoning topic. The task is simple: given a sequence of numbers, letters, or figures following a hidden pattern, identify the next term or the missing term. This tests your ability to spot patterns quickly and apply logical rules under time pressure.

Key ideas

• Arithmetic Series: Each term differs from the previous by a constant value (common difference). Example: 3, 7, 11, 15, 19 → difference is +4.
• Geometric Series: Each term is multiplied by a constant value (common ratio). Example: 2, 6, 18, 54 → ratio is ×3.
• Square/Cube Series: Terms are perfect squares (1, 4, 9, 16, 25) or perfect cubes (1, 8, 27, 64, 125), sometimes with additions or subtractions.
• Difference of Differences: When first-level differences vary, check second-level differences. If those are constant, it's a quadratic pattern.
• Letter Series by Position: A=1, B=2, ... Z=26. Patterns involve adding/subtracting positions. Example: B, E, H, K → positions 2, 5, 8, 11 (difference +3).

Watch out for

• Jumping to conclusions after two terms → Always verify your pattern holds for at least 3–4 consecutive terms before selecting the answer.
• Ignoring second-level differences → When first differences aren't constant, students give up. Check differences of differences—this catches quadratic patterns.
• Miscounting letter positions → Students often miscount beyond M. Memorise: M=13, N=14, and work from there. Also remember Z=26 wraps to A=1 in cyclic series.

Quick reference

• No constant difference? Check difference of differences.
• Letters: Convert to numbers, find pattern, convert back.
• Alternating series: Split into odd-position and even-position sub-series.
• Near squares/cubes? Test n² ± k or n³ ± k.
• Prime series terms: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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