Number Series - Formula Sheet
🔢 Number Series - Formula Sheet
🎯 Basic Patterns
Arithmetic Progression (AP)
Common difference (d) constant Formula: a, a+d, a+2d, a+3d, … Example: 3, 7, 11, 15, 19 (d=4)
Geometric Progression (GP)
Common ratio (r) constant Formula: a, ar, ar², ar³, … Example: 2, 6, 18, 54, 162 (r=3)
Squares/Cubes
Perfect squares: 1, 4, 9, 16, 25 Perfect cubes: 1, 8, 27, 64, 125 Square + 1: 2, 5, 10, 17, 26 Cube - 1: 0, 7, 26, 63, 124
📊 Advanced Patterns
Alternating Series
Two interleaved patterns Example: 2, 8, 4, 16, 6, 24 Pattern 1: 2, 4, 6 (+2) Pattern 2: 8, 16, 24 (+8)
Product/Sum Patterns
Multiplication: 2, 6, 18, 54 (×3) Addition + Multiplication: 2, 4, 12, 48 (+2, ×3, ×4) Square operations: 2, 4, 16, 256 (×2, ×4, ×16)
Digit Operations
Digit sum: 23, 5, 14, 5, 17, 8 Digit product: 34, 12, 26, 12, 39, 27 Alternating digits: 1234, 13, 24, 37, 11
🔢 Special Series
Fibonacci Series
Sum of previous two terms Example: 0, 1, 1, 2, 3, 5, 8, 13
Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23
Factorial Series
1!, 2!, 3!, 4!, 5! 1, 2, 6, 24, 120
Triangular Numbers
1, 3, 6, 10, 15, 21 Formula: n(n+1)/2
⚡ Complex Patterns
Multiple Operations
Pattern: ×2+1, ×2+2, ×2+3, … Example: 3, 7, 16, 35, 72 3×2+1=7, 7×2+2=16, 16×2+3=35, 35×2+2=72
Position-based
Square positions: 1², 2², 3², 4² Cube positions: 1³, 2³, 3³, 4³ Prime positions: 2nd, 3rd, 5th, 7th terms
Difference Patterns
Second order difference constant: Original: 2, 5, 10, 17, 26 1st diff: 3, 5, 7, 9 2nd diff: 2, 2, 2 (constant)
📝 Solving Strategy
Step-by-Step Approach
- Check basic patterns (AP, GP)
- Look for squares/cubes
- Check alternating patterns
- Examine differences between terms
- Try product/sum patterns
- Consider digit operations
- Verify pattern throughout
Quick Checks
Differences: Constant or pattern? Ratios: Constant or pattern? Special numbers: Primes, squares, cubes? Alternating: Two separate patterns?
🔍 Common Question Types
Missing Number
Find the missing term in sequence Example: 2, 5, ?, 17, 26 (Answer: 10)
Wrong Number
Identify number that doesn’t fit pattern Example: 2, 4, 8, 17, 32 (17 is wrong, should be 16)
Next Number
Find the next term in sequence Example: 3, 7, 15, 31, ? (Answer: 63)
⚡ Quick Tips
Pattern Recognition
- Always check simple patterns first
- Calculate differences between terms
- Look for multiplication patterns
- Consider digit-based patterns
- Check for alternating patterns
Common Mistakes to Avoid
Don’t assume pattern too early Check pattern with all given terms Consider multiple possibilities Verify answer fits complete pattern
Time Management
- Quick scan for obvious patterns
- Systematic checking of common patterns
- Skip very complex patterns initially
- Return if time permits
📚 Practice Areas
Mental Calculation
Quick multiplication/division Square and cube calculations Digit sum operations
Pattern Recognition
Common mathematical sequences Visual pattern identification Logical reasoning skills
Master Number Series - Pattern, verify, apply! 🔢
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