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Number Series

UP Police Constable · Quantitative Aptitude

Also prepare for:CRPF Const BSF Const CISF Const ITBP Const

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Core Concept

Read this first — the foundation of the topic

→Arithmetic Series

Each term increases or decreases by a constant difference

✏️Example

5, 8, 11, 14 (difference = +3) 2

→Geometric Series

Each term is multiplied by a constant ratio

✏️Example

2, 6, 18, 54 (ratio = ×3) 3. Square/Cube Series: Based on squares or cubes of consecutive numbers

✏️Example

1, 4, 9, 16 (1², 2², 3², 4²) 4

→Prime Number Series

Following prime number sequence 5

→Mixed Operations

Combination of addition, subtraction, multiplication, division 6. Double/Triple Layer Series: Two or three different patterns running simultaneously

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Exam Patterns

What examiners ask — read before attempting PYQs

SSC CGL typically asks 2-3 questions on number series. Common question types include finding the missing term, identifying the wrong number, or completing the series. The difficulty ranges from simple arithmetic progressions to complex mixed operation patterns. Powerful Shortcut - The Difference Method: Write differences between consecutive terms. If first-level differences don't show pattern, find second-level differences (differences of differences).

Most SSC series get solved within 2-3 levels.

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Worked Example

Solve this step-by-step before moving on

1

Step 1

Find first-level differences 7-3 = 4 15-7 = 8 31-15 = 16 ? -31 = ? 127-? = ?

2

Step 2

Observe the difference pattern 4, 8, 16, ?, ? This is a geometric series with ratio 2 Next difference = 16 × 2 = 32 Following difference = 32 × 2 = 64

3

Step 3

Find the missing number ? = 31 + 32 = 63 Verify: 127 - 63 = 64 ✓ Answer: 63 Quick Trick for Square Series: If you see numbers like 2, 5, 10, 17, 26, check if they follow n² + 1 pattern: 1² + 1 = 2 2² + 1 = 5 3² + 1 = 10 4² + 1 = 17 5² + 1 = 26 Common Mistake: Students often assume the first pattern they see is correct. Always verify your answer by checking if it fits the complete series. In mixed operation series, don't stop at first-level differences - go deeper if needed.

🔑 Key Points

Number series questions appear 2-3 times in SSC CGL with moderate to high difficulty
Use difference method: find differences between consecutive terms to identify pattern
Arithmetic series have constant difference, geometric series have constant ratio
Square series follow pattern n², n²+1, n²-1, or similar variations
Prime number series: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Mixed operation series combine addition, subtraction, multiplication, division patterns
Double layer series have two different patterns running simultaneously
Always verify your answer by checking if it satisfies the complete series pattern

📌 Exam Facts

First 10 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Perfect squares up to 15²: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Perfect cubes up to 10³: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Fibonacci series starts: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
Common ratios in geometric series: ×2, ×3, ×0.5, ×1.5, ×4
Triangular numbers: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55
Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024
Most SSC number series can be solved using maximum 3 levels of differences

🚀 60-Second Revision

Remember: Apply difference method first - find differences between consecutive terms
Formula: For arithmetic series, nth term = a + (n-1)d where a=first term, d=common difference
Trick: If first differences don't work, try second-level differences immediately
Pattern: Check for squares (n²), cubes (n³), or modified versions (n²±k)
Trap: Don't assume first pattern you see is correct - always verify with complete series
Speed: Memorize first 15 squares, 10 cubes, and 10 prime numbers
Strategy: For geometric series, check if ratio is consistent throughout the sequence

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Test yourself under real exam conditions

A timed UP Police Constable mock shows exactly how Number Series questions appear in the actual paper — and where you lose marks.

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