Number Series – Aptitude Concepts and Formulas

A number series is a sequence of numbers arranged according to a specific rule or pattern. Your task is to identify the rule and either:

• Find the next number, or
• Find the missing number in the sequence.

Common Types of Number Series

Type	Pattern/Rule	Example	Explanation
Arithmetic Series	Each term increases/decreases by a fixed number (common difference)	2, 5, 8, 11, 14, ?	+3 each time → Next = 17
Geometric Series	Each term multiplied/divided by a fixed number (common ratio)	3, 6, 12, 24, ?	×2 each time → Next = 48
Square/Cube Series	Terms are squares or cubes of consecutive numbers	1, 4, 9, 16, 25, ?	Squares → Next = 36
Alternating Pattern	Two or more sub-series interleaved	2, 4, 8, 3, 6, 12, 4, ?	Alternate ×2 and +1 pattern
Mixed Operations	Combination of +, −, ×, ÷	5, 10, 9, 18, 17, 34, ?	×2, −1 alternately
Prime Number Series	Terms are prime numbers or follow prime differences	2, 3, 5, 7, 11, 13, ?	Next = 17
Fibonacci Series	Each term = Sum of previous two terms	1, 1, 2, 3, 5, 8, ?	Next = 13
Difference Pattern	Look at first-level or second-level differences	3, 6, 11, 18, 27, ?	Differences: +3, +5, +7, +9 → Next = 38
Multiplication + Addition Pattern	Mix of × and + operations	2, 5, 11, 23, 47, ?	×2 +1 each time → Next = 95
Division Pattern	Terms reduce by dividing by a constant or pattern	128, 64, 32, 16, ?	÷2 → Next = 8

Step-by-Step Strategy to Solve

1. Check for simple patterns → +n, −n, ×n, ÷n
2. Observe differences – first-level or second-level; constant → quadratic
3. Check for alternating patterns (odd/even position trends)
4. See for squares/cubes/factorials (e.g. n² pattern)
5. Check for primes or Fibonacci type
6. Test mixed operations (e.g. ×2 +1, ×3 −2)
7. Verify by backtracking to confirm the logic

Advanced Series Patterns

Type	Example	Explanation
Quadratic Pattern	2, 6, 12, 20, 30, ?	Differences = 4,6,8,10 → Next = 42
Cubic Pattern	1, 8, 27, 64, ?	n³ → Next = 125
Power-based	2, 4, 8, 16, 32	2ⁿ pattern
Position Pattern	10, 21, 43, 87, ?	×2 +1
Mixed Alternate	1, 2, 4, 7, 11, 16, 22, ?	+1, +2, +3, +4, +5, +6 → Next = 29
Complex Nested	3, 6, 12, 24, 48, 96	Simple doubling
Pattern in Digits	131, 1331, 13331, 133331	Increasing 3’s inside pattern

Common Tricky Series (Exam Favorites)

Example	Logic
3, 9, 27, 81, ?	×3 → 243
7, 10, 8, 11, 9, 12, ?	Alternating +3, −2 → Next = 10
121, 225, 361, 529, ?	(11², 15², 19², 23², …) → Next = 27² = 729
1, 4, 3, 9, 5, 16, 7, ?	Squares in even places → 25
2, 12, 30, 56, 90, ?	Differences 10,18,26,34 → +8 each → Next diff=42 → 132

Tips & Tricks

• Write down differences clearly.
• Identify if pattern alternates.
• Try backward reasoning if stuck.
• Watch out for square/cube/primes — very common in banking/SSC.
• In CAT-level questions, patterns are often multi-layered (e.g., alternate +, ×).

Commonly Asked Questions

Exam	Common Pattern Type	Example
Bank PO / Clerk	Arithmetic / Geometric / Alternate	5, 10, 20, 40, ?
SSC CGL / CHSL	Squares / Cubes / Prime / Mixed	1, 8, 27, ?
Placement Aptitude	Logical & Alternating	3, 5, 9, 17, 33, ?
CAT / XAT / OMETs	Complex multi-step logic	2, 6, 18, 54, 162, ?

Practice Questions

1. 7, 14, 28, 56, ?
2. 4, 9, 19, 39, 79, ?
3. 2, 6, 12, 20, 30, ?
4. 3, 6, 12, 24, 48, ?
5. 1, 1, 2, 3, 5, 8, ?
6. 121, 144, 169, 196, ?
7. 13, 17, 23, 31, 41, ?

Answers: 1) 112 2) 159 3) 42 4) 96 5) 13 6) 225 7) 53

Shortcut Summary Table

Operation	Symbol	Example	Note
Addition	+	2, 5, 8, 11	Arithmetic
Multiplication	×	2, 4, 8, 16	Geometric
Power	^	2, 4, 8, 16	Exponential
Alternate	Alt	1, 4, 2, 5, 3, 6	Odd–even subseries
Difference Pattern	Δ	1, 4, 9, 16	Second diff constant
Prime	P	2, 3, 5, 7	Prime numbers
Fibonacci	F	1, 1, 2, 3, 5	Add previous two

Final Exam Tips

• Always write terms vertically to spot differences faster.
• Spend max 30 seconds per question in timed exams.
• Practice 500+ series to master all pattern types.
• Use elimination — often only one option fits the logic.

Refer Aptitude Concepts

Practice Aptitude Questions on Number Series