12. Number Series Basics

SSC/RRB frequently test the ability to spot the underlying pattern in a sequence of numbers and either find the next term or find the “odd one out.” These questions lean directly on the number-theory tools already covered in this chapter: divisibility, squares/cubes, primes, and simple arithmetic/geometric patterns.

Common series patterns to check, in order of frequency: 1. Arithmetic series — constant difference between consecutive terms (e.g., 5, 9, 13, 17, … difference +4). 2. Geometric series — constant ratio between consecutive terms (e.g., 3, 6, 12, 24, … ratio ×2). 3. Squares/cubes series — terms are n², n³, or n²±k (e.g., 2, 5, 10, 17, 26 → n²+1 for n=1,2,3,4,5). 4. Difference-of-differences (second-order) series — the differences themselves form a pattern (e.g., 2, 3, 6, 11, 18 → differences 1,3,5,7 — an arithmetic series of differences). 5. Alternating/two-interleaved series — odd positions follow one rule, even positions follow another (e.g., 3, 20, 5, 18, 7, 16 → odd positions increase by 2, even positions decrease by 2). 6. Prime number series — consecutive primes, or primes with an operation applied. 7. Multiplication-and-addition mixed series — e.g., ×2+1, ×2+2, ×2+3… (2, 5, 12, 27, 58…).

Why it works / exam approach: Always compute the first-level difference between consecutive terms first. If it’s constant, it’s arithmetic. If not constant but the differences themselves show a pattern, check second-level differences. If differences grow multiplicatively, suspect a ratio or squares/cubes pattern instead.