Number Series
Types of Series
1. Arithmetic Progression (AP)
- Pattern: Each term increases/decreases by constant difference
- Example: 2, 5, 8, 11, 14... (difference = 3)
- nth term: a + (n-1)d
- Sum of n terms: n/2[2a + (n-1)d]
2. Geometric Progression (GP)
- Pattern: Each term multiplied by constant ratio
- Example: 2, 6, 18, 54... (ratio = 3)
- nth term: a × r^(n-1)
- Sum of n terms: a(r^n - 1)/(r - 1)
3. Square Series
- Pattern: Squares of consecutive numbers
- Example: 1, 4, 9, 16, 25... (1², 2², 3², 4², 5²)
4. Cube Series
- Pattern: Cubes of consecutive numbers
- Example: 1, 8, 27, 64, 125... (1³, 2³, 3³, 4³, 5³)
5. Prime Number Series
- Example: 2, 3, 5, 7, 11, 13, 17, 19, 23...
6. Fibonacci Series
- Pattern: Sum of previous two terms
- Example: 0, 1, 1, 2, 3, 5, 8, 13, 21...
7. Mixed Series
- Alternating patterns: +5, -2, +5, -2...
- Two series mixed: Odd and even positions follow different patterns
Solving Techniques
- Find difference between consecutive terms
- Check for multiplication/division pattern
- Look for squares, cubes, prime numbers
- Check alternating patterns
- Verify the pattern for all terms
Quick Tips
- Always check differences and ratios first
- Look for mathematical operations between terms
- Practice identifying patterns quickly
- Memorize squares up to 30 and cubes up to 15