Number Series Patterns and Problem Solving

Jul 21, 2024

Number Series - Lecture Notes

Importance

  • The stronger you are in number series, the better your reasoning will be.
  • Understanding number series helps in various reasoning questions.

Basic Concept

  • Identify the pattern between a set of numbers and guess the next number.
  • Example:
    • 2, 4, 6, 8 - Here, the pattern is to add 2 to each number.

Types of Series

  • Square Series: Example: 1^2, 2^2, 3^2, 4^2
  • Cubes Series: Example: 1^3, 2^3, 3^3, 4^3
  • Odd Number Series: Such as 1, 3, 5, 7

Problem Solving - Steps

  1. Check the Difference: If the series isn’t clear, look at the differences between numbers.
    • Example: 2, 15, 41, 80
    • Differences: 13, 26, 39 (Multiples of 13)
  2. Check Patterns of Squares/Cubes:
    • If nothing is clear from the differences, check for patterns of squares or cubes.
  3. Multiplication or Other Operations: Like using multiplication for a series with large growth.
    • Example: 32, 87, 332, 1335 (Here, there could be a multiplication pattern)

Patterns of Increasing Numbers

  • If the numbers are rapidly increasing, suspect multiplication.
  • Example:
    • 3287, 9876, 5635: Can be solved using a multiplication pattern

Special Examples

  • When patterns are formed by adding squares and cubes together.
    • Such as: 4, 9, 16, 25 (Series of squares)
    • Subtract 1, 2, 3, etc., in between: 3, 7, 12, 21

Practical Approach

  • When nothing is clear, check differences or try multiplying larger numbers.

Understanding GP and AP

  • GP (Geometric Progression): Multiplying by a fixed ratio
    • Example: 5, 10, 20, 40 (Ratio=2)
  • AP (Arithmetic Progression): Adding a constant difference
    • Example: 1, 3, 5, 7 (Difference=2)

Advice

  • Remember square and cube series up to 20.
  • Quickly identify patterns by finding the differences.
  • Practice as much as possible to solve various types of series.

Final Points to Remember

  • Don’t get intimidated by large numbers; they can be solved using simple rules and operations.
  • Repeatedly practice multiplication patterns and square/cube patterns.
  • Use practice sheets and approach someone to clear any doubts.

In the Next Video:

  • Examples of more complex series and their solutions.
  • Cover patterns beyond squares and cubes.