Logical Reasoning: Number Series

Concept Explanation

A number series is a sequence of numbers built from a fixed rule. Placement and bank exams usually ask for the missing term or the wrong term. Most patterns come from a short list of ideas — once you spot the rule, the rest is quick arithmetic.

Common patterns

• Constant difference (AP): each term changes by the same amount (e.g. +3, +3, +3).
• Constant ratio (GP): each term is multiplied by the same factor (e.g. ×2, ×2, ×2).
• Second-order difference: differences of differences are constant (common in 1, 4, 9, 16, … style builds).
• Squares / cubes / primes: terms are n², n³, or consecutive primes.
• Mix patterns: alternate rules (×2 then +1), or combine two simple series interleaved.

How to solve fast

1. Write first differences between neighbours; if not constant, write second differences.
2. Check if terms look like squares, cubes, or multiples of a base.
3. For long series, test alternate positions (odd-index vs even-index rules).