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Number Series

About 6 min · Numerical & Mental Ability · English

Time worked out from the lesson's 345 words at 150 words a minute, plus a minute for each question.

The task is straightforward: identify patterns in a sequence of numbers and either find the next term, spot the wrong term, or fill a missing term. Mastery of this topic demands sharp observation and quick pattern recognition, both crucial for time-bound competitive exams.

Key ideas

• Arithmetic Series: Each term is obtained by adding (or subtracting) a constant difference to the previous term. Example: 3, 7, 11, 15 (difference = +4).
• Geometric Series: Each term is obtained by multiplying (or dividing) the previous term by a constant ratio. Example: 2, 6, 18, 54 (ratio = ×3).
• Square and Cube Series: Terms follow perfect squares (1, 4, 9, 16, 25) or perfect cubes (1, 8, 27, 64, 125), sometimes with slight addition/subtraction.
• Prime Number Series: Sequence consists of prime numbers in ascending order: 2, 3, 5, 7, 11, 13, 17, 19, 23...
• Alternate Series: Two independent patterns run alternately. Odd-positioned and even-positioned terms follow separate rules.

Watch out for

• Assuming only one pattern type: Students often check only arithmetic progression and miss geometric or mixed patterns. Fix: Always check differences first; if inconsistent, check ratios or second-level differences immediately.
• Ignoring alternate series: When differences oscillate wildly, students try to force a single pattern. Fix: Split the series into odd and even positions and analyze separately.
• Calculation errors with squares/cubes: Misremembering 17² = 289 as 279 or 13³ = 2197 as 2179 leads to wrong answers. Fix: Drill multiplication tables and perfect squares/cubes until automatic.

Quick reference

• Arithmetic series → constant difference between consecutive terms (check with subtraction).
• Geometric series → constant ratio between consecutive terms (check with division).
• Alternate series → split into two independent sequences by position.
• Square/cube series → check if terms match n², n³ or n² ± k pattern.
• Difference-of-difference → when first differences vary, compute second-level differences.

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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