Number Series
Why This Chapter Matters
Number Series questions appear in every banking exam — 5-10 marks. You need to identify the pattern quickly (usually within 30-60 seconds per question) and find the missing/wrong term.
Types of Number Series
1. Arithmetic Series
Constant difference between terms.
Example: 5, 8, 11, 14, 17... (diff = +3)
Example: 20, 16, 12, 8... (diff = -4)
2. Geometric Series
Constant ratio between terms.
Example: 3, 6, 12, 24, 48... (ratio = x2)
Example: 243, 81, 27, 9, 3... (ratio = /3)
3. Difference Series
Differences between terms form a pattern.
Example: 2, 3, 5, 8, 12, 17... (differences: 1,2,3,4,5)
Example: 1, 4, 9, 16, 25... (perfect squares; differences: 3,5,7,9)
4. Mixed Series
Alternating two different patterns.
Example: 1, 2, 4, 8, 7, 14... (alternating x2 and +3 or something)
5. Square/Cube Based
n^2 ± something: 2, 5, 10, 17, 26 (n^2+1 for n=1,2,3,4,5)
n^3 patterns: 1, 8, 27, 64, 125...
6. Prime Number Based
2, 3, 5, 7, 11, 13, 17, 19, 23...
7. Wrong Number in Series
Find which term doesn't fit the pattern.
Check each term against the pattern. The outlier is the wrong number.
Approach Strategy
Step 1: Check for simple AP (constant difference). Calculate 5 differences.
Step 2: If not AP, check for GP (constant ratio).
Step 3: Check if differences form a pattern (difference series).
Step 4: Check for squares, cubes, primes.
Step 5: Look for two alternating patterns.
Practice Examples
Q1: 3, 7, 13, 21, 31, ?
Differences: 4, 6, 8, 10, 12. Next term: 31+12 = 43.
Q2: 4, 9, 25, 49, 121, ?
Squares of primes: 2^2, 3^2, 5^2, 7^2, 11^2. Next: 13^2 = 169.
Q3: 2, 3, 6, 11, 18, ?
Differences: 1, 3, 5, 7. Next difference = 9. Next term = 18+9 = 27.
Q4: 8, 12, 16, 21, 27, 34, ? (Wrong number series)
Pattern: +4, +4, +5, +6, +7, +8. So 16 should be followed by 16+5=21, 21+6=27 etc. But 8+4=12, 12+4=16, 16+5=21 ✓ correct. Let me check: diff = 4,4,5,6,7. 12 to 16 = 4 ✓. All look fine. Maybe pattern is +4, +4, +4... and 21 should be 20. Wrong number = 21 (should be 20).
Q5 (Bank pattern): 5, 10, 40, 240, ?
Ratios: x2, x4, x6. Pattern: multiply by 2,4,6,8... Next: 240 x 8 = 1920.
Previous Year Questions
SBI Clerk 2023: 11, 22, 66, 264, ?
Multiply by: 2, 3, 4, 5. Next: 264 x 5 = 1320.
IBPS PO 2022: Find wrong number: 3, 7, 15, 27, 63, 127
Differences: 4,8,12,36,64 — not consistent. Pattern should be: 3, 7, 15, 31, 63, 127 (each = 2x previous + 1). So 27 is wrong; should be 31.
RRB 2021: ?, 4, 9, 16, 25, 36
Missing is 1 (series of n^2: 1,4,9,16,25,36).