Introduction

This guide covers the Number Series topic for All Exams aspirants. Master the concept, understand the tricks, and then test yourself with 10 practice MCQs.

Number Series — Concept Guide

Number series questions ask you to find the next term, missing term, or wrong term in a sequence. Mastering these requires recognising common patterns quickly.

Pattern Types to Master

  • Arithmetic: Equal differences (2,5,8,11 → +3)
  • Geometric: Equal ratios (2,6,18,54 → ×3)
  • Squares/Cubes: 1,4,9,16,25 / 1,8,27,64
  • Fibonacci: 1,1,2,3,5,8,13 (sum of two before)
  • Two-step: ×2+1, ×2-1 patterns
  • Double difference: Differences of differences are constant

⚡ Shortcuts & Tricks

  • Step 1: Calculate differences. Step 2: If not constant, find differences of differences.
  • Memorise squares: 1 to 30 and cubes: 1 to 20 for instant recognition.
  • Prime number series: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47...
  • For alternating series: check odd-positioned and even-positioned terms separately.
  • Tip: try ×2, ×3, +prime, +consecutive odd numbers as your first checks.

Practice MCQs — Number Series (10 Questions)

Now test your understanding with these 10 questions:

Q1. What comes next: 2, 6, 18, 54?

  • A. 162
  • B. 108
  • C. 216
  • D. 72
Answer: A — Multiply by 3. 54×3=162.

Q2. 1, 4, 9, 16, 25, next?

  • A. 36
  • B. 30
  • C. 32
  • D. 34
Answer: A — Perfect squares. 6²=36.

Q3. 5, 10, 20, 40, next?

  • A. 80
  • B. 60
  • C. 100
  • D. 70
Answer: A — ×2 each time. 40×2=80.

Q4. 100, 90, 81, 73, 66, next?

  • A. 60
  • B. 59
  • C. 62
  • D. 58
Answer: A — Differences: 10,9,8,7,6. 66-6=60.

Q5. 3, 8, 15, 24, 35, next?

  • A. 48
  • B. 44
  • C. 50
  • D. 52
Answer: A — Differences: 5,7,9,11,13. 35+13=48.

Q6. 1, 1, 2, 3, 5, 8, 13, next?

  • A. 21
  • B. 18
  • C. 20
  • D. 22
Answer: A — Fibonacci: 8+13=21.

Q7. 7, 13, 25, 49, 97, next?

  • A. 193
  • B. 190
  • C. 195
  • D. 200
Answer: A — ×2 – 1 pattern. 97×2-1=193.

Q8. 2, 12, 36, 80, 150, next?

  • A. 252
  • B. 240
  • C. 260
  • D. 270
Answer: A — n²(n+1): 2=1²×2, 12=2²×3, 36=3²×4, 80=4²×5, 150=5²×6, 252=6²×7.

Q9. 4, 9, 25, 49, 121, next?

  • A. 169
  • B. 144
  • C. 196
  • D. 225
Answer: A — Squares of primes: 2²,3²,5²,7²,11²,13²=169.

Q10. 11, 13, 17, 19, 23, next?

  • A. 29
  • B. 25
  • C. 27
  • D. 31
Answer: A — Prime numbers sequence. Next prime after 23 = 29.

Summary

Number Series is a scoring topic in All Exams if you practise consistently. Focus on understanding the concept, apply the shortcut tricks, and practice regularly. Aim for 100% accuracy in this topic through regular revision.