Number and Letter Series
Overview
Number and Letter Series is one of the most frequently asked topics in Railway NTPC and Group D exams. Questions test a candidate's ability to identify patterns in sequences of numbers, letters, or both. Patterns include arithmetic progressions, geometric progressions, prime numbers, squares, cubes, alternating differences, and mixed series. Mastering common patterns and practicing speed-solving techniques is essential to score full marks in this chapter.
Typed Notes
Types of Number Series
Railway exams test six main number series types. (1) Arithmetic: constant addition/subtraction — e.g., 5, 10, 15, 20. (2) Geometric: constant multiplication/division — e.g., 3, 9, 27, 81. (3) Square/Cube series — e.g., 1, 8, 27, 64. (4) Prime number series — e.g., 2, 3, 5, 7, 11, 13. (5) Fibonacci-type: each term = sum of previous two — e.g., 1, 1, 2, 3, 5, 8. (6) Difference series: differences themselves form a pattern — e.g., 2, 3, 5, 9, 17 (differences: 1, 2, 4, 8 — doubling). Exam Tip: Always write differences between consecutive terms first; this reveals the hidden pattern within 10 seconds.
Letter Series Techniques
Every letter has a fixed position: A=1, B=2 … Z=26. Memorise EJOTY (5,10,15,20,25) as a quick reference hook. In Railway papers, common patterns are: (1) Skip-one series — A, C, E, G (every alternate letter). (2) Skip-two series — A, D, G, J (+3 each time). (3) Reverse alphabet series — Z, Y, X, W. (4) Opposite pairs — A↔Z, B↔Y (sum always 27). Questions often ask the 'odd one out' or 'missing letter.' Always convert letters to numbers, find the numeric pattern, then convert back. This eliminates confusion with tricky sequences.
Alphanumeric and Wrong Term Series
Alphanumeric series combine letters and numbers. Solve letter and number parts separately. Example: B4, D9, F16, H25 — letters skip one (+2), numbers are squares (4,9,16,25). Wrong-term series (find the odd one out) are very common in NTPC. Strategy: check all five terms; find where the pattern breaks. Example: 2, 5, 10, 17, 26, 36, 50 — differences are 3,5,7,9,11,13 (odd numbers). Term 36 should be 37 (26+11=37), so 36 is wrong. Exam Tip: In wrong-term questions, never guess — always verify the term before and after the suspected wrong number.
Speed Tricks and Common Patterns to Memorise
Memorise these ready patterns for Railway exams: Squares up to 30 (1 to 900), Cubes up to 15 (1 to 3375), Prime numbers up to 100 (25 primes). Key trick — 'Second Difference Method': if first differences are not constant, find differences of differences; if those are constant, it is a quadratic series. Example: 3, 6, 11, 18, 27 — first diff: 3,5,7,9 — second diff: 2,2,2 (constant) → quadratic. For letter series, use EJOTY hook to jump quickly to mid-alphabet letters. Time target: solve each series question in under 45 seconds in the exam.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Arithmetic Series: Each term differs by a constant value (common difference), e.g., 3, 7, 11, 15 — difference is +4 throughout.
- 02Geometric Series: Each term is multiplied by a constant ratio, e.g., 2, 6, 18, 54 — ratio is ×3 throughout.
- 03Perfect Squares and Cubes Series: 1, 4, 9, 16, 25 (squares) and 1, 8, 27, 64, 125 (cubes) appear very frequently in Railway papers.
- 04Letter Series: Based on alphabetical position (A=1, Z=26); patterns involve skipping letters, reversing, or alternating steps, e.g., A, C, F, J — gaps are +2, +3, +4.
- 05Mixed/Alphanumeric Series: Combination of letters and numbers following independent or interlinked patterns, e.g., A2, C4, E6, G8 — letters skip one, numbers increase by 2.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Find the missing term: 4, 9, 25, 49, ?, 169
Find the wrong term: 1, 5, 14, 30, 55, 90, 140
Find the missing letter: B, E, H, K, ?
Find the missing term in the alphanumeric series: Z1, X4, V9, T16, ?
What comes next: 2, 3, 5, 8, 13, 21, ?
Number and Letter Series questions in Railway NTPC and Group D follow predictable patterns — arithmetic, geometric, squares, cubes, primes, Fibonacci, and letter-position rules. The key strategy is to write differences first, use the EJOTY memory hook for letters, and memorise squares up to 30 and cubes up to 15. Wrong-term series require verifying surrounding terms. With regular practice, each question can be solved in under 45 seconds.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Which term is wrong in the series: 3, 7, 15, 27, 63, 127?
Q2.Find the missing term: A, D, I, P, ?
Q3.What is the next number: 1, 8, 27, 64, 125, ?
Q4.In the series 6, 11, 21, 41, 81, ?, each term is obtained by:
Mark karo — dashboard par progress dikhega.