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.

Analogy — Think of a number series like a short piece of music with a repeating rhythm — once you've identified the pattern in the first 2-3 "beats" (the gap between consecutive terms), the rest of the sequence is just continuing that same rhythm, not a fresh puzzle each time. Checking the differences between consecutive terms first (is it constant? growing? doubling?) is exactly like listening for the beat before trying to guess the next note.

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).

Revision Notes

SERIES TYPES (check in order):
1. AP (constant difference)
2. GP (constant ratio)
3. Difference pattern (differences form series)
4. Square/cube pattern
5. Prime based
6. Two alternating patterns

COMMON PATTERNS TO RECOGNIZE:
Perfect squares: 1,4,9,16,25,36,49,64,81,100
Perfect cubes: 1,8,27,64,125,216,343
Primes: 2,3,5,7,11,13,17,19,23,29,31,37

WRONG NUMBER: find which term breaks the pattern
- Usually the error is ±1 or a small difference from the correct value

Try It (2 Minutes)

Series: 3, 7, 15, 31, 63, ?. Before checking any formula, find the "rhythm" between consecutive terms yourself: 7-3=4, 15-7=8, 31-15=16, 63-31=32 — each gap doubles. Continuing that rhythm, the next gap should be 64, so the answer is 63+64=127. Notice you found this purely by listening for the repeating pattern in the differences, not by matching it to a memorized series "type."