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Number Series

About 5 min · Numerical Ability · English

Time worked out from the lesson's 282 words at 150 words a minute, plus a minute for each question.

These questions test your ability to identify patterns in sequences of numbers and either find the missing term or spot the wrong term that breaks the pattern.

Key ideas

• Arithmetic Series (Constant Difference): Each term differs from the previous by a fixed number. Example: 3, 7, 11, 15, 19 (difference = +4).
• Geometric Series (Constant Ratio): Each term is multiplied by a fixed number. Example: 2, 6, 18, 54, 162 (ratio = ×3).
• Square-Based Series: Terms follow a pattern involving perfect squares (1, 4, 9, 16, 25...) either as terms themselves or as differences.
• Cube-Based Series: Terms follow patterns involving perfect cubes (1, 8, 27, 64, 125...).
• Two-Step Patterns: The difference between terms itself forms a pattern. Example: Differences of 2, 4, 6, 8... (increasing by 2).

Watch out for

• Jumping to conclusions after checking only 2 terms → Always verify your pattern holds for at least 3–4 transitions before answering.
• Confusing multiplication and addition patterns → If numbers grow slowly, think addition; if they grow rapidly, think multiplication or powers.
• Forgetting mixed operations → Don't assume a single operation. Try combinations like ×2 + 1, or alternating +/×.

Quick reference

• First step: Always calculate differences between consecutive terms.
• If differences are constant: Arithmetic series (add the same number).
• If ratios are constant: Geometric series (multiply by the same number).
• If differences increase uniformly: Second-level arithmetic (differences of differences).
• Large jumps between terms: Think multiplication, squares, or cubes.

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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