Number Series & Quadratic Equations

Syllabus Unit: Quantitative Aptitude

Why it matters

Chapter overview

Number Series and Quadratic Equations form the 'speed' section of SBI PO Quant — typically five questions each that reward pattern recognition and formula recall over lengthy calculation. This topic covers spotting the logic in a number series (including the one wrong term), solving quadratics and linear equations to compare two variables, and the coded-inequality format that dresses up basic inequality logic in symbols.

Preliminary Examination Syllabus Quantitative Aptitude 35% weightage

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1List the TermsWrite all given values in a row

2Find Differences/RatiosCompute T2−T1, T3−T2, ...

3Spot the RuleMatch to a known pattern type

4Apply & VerifyTest the rule on every term

1Missing & Wrong Number Series

Every number series hides one arithmetic rule — find the pattern in the differences, ratios, or squares before hunting for the missing or wrong term.

Learning Objectives

Identify the common series patterns: arithmetic difference, geometric ratio, squares/cubes, alternating operations, and difference-of-differences.
Distinguish a 'missing number' series (find the blank) from a 'wrong number' series (find the term that breaks the pattern).
Compute successive differences quickly to reveal a hidden arithmetic or quadratic progression.
Verify a suspected pattern against at least four terms before committing to an answer.

Key Terms

Difference SeriesA series where consecutive differences themselves form a pattern (e.g., 2,3,4,5,... or 2,4,8,16...) rather than staying constant.

Wrong Number SeriesA series in which every term fits a rule except one; the task is to find that single incorrect term, not compute a missing one.

nth-term FormulaAn algebraic expression like n²+2n or n³−1 that generates every term directly from its position n — common in square/cube-based series.

Alternating SeriesA series that applies two different operations in alternating turns (e.g., ×2, +3, ×2, +3, ...).

A number series question gives 5-6 terms following one hidden rule and asks for a missing term or the one term that breaks the rule. The entire question is solved the moment the rule is spotted — the arithmetic after that is trivial.

Patterns to check first, in order

Constant or increasing/decreasing difference — 5, 9, 13, 17 (+4 each time) or 2, 5, 9, 14 (+3, +4, +5).
Constant or changing ratio — 3, 6, 12, 24 (×2 each time) or 2, 6, 24, 120 (×3, ×4, ×5 — factorial-style).
Squares, cubes, or n²±n patterns — 1, 4, 9, 16 or 2, 8, 18, 32 (2n²).
Alternating two operations — 5, 10, 8, 16, 14 (×2, −2, ×2, −2, ...).
Prime number sequences or two interleaved series (odd positions follow one rule, even positions another).

Check: T2−T1, T3−T2, T4−T3, … — then check if THAT sequence of differences has its own pattern (difference-of-differences).

Missing vs wrong number series

Missing number — find the pattern from the given terms, then apply it once to generate the blank.
Wrong number — assume the pattern from the first 2-3 terms, then test every remaining term against it; the term that fails is the answer.

Common MistakeIn a wrong-number series, the error is more often planted in the middle (3rd or 4th term) than at the very end — don't stop checking once the last term matches.

Exam TipCompute just the first two differences and the first two ratios mentally — this alone eliminates most of the six pattern types in seconds.