08

Phase 2 - Level 3: Mathematical & Logical Patterns

Chapter 8 • Intermediate

90 min

Phase 2 - Level 3: Mathematical & Logical Patterns

Introduction

This level focuses on mathematical sequences, series, and logical patterns. You'll learn to generate sequences, calculate series sums, and recognize patterns in mathematical problems.

Key Concepts

Mathematical Series

  • Arithmetic Progression (AP): Sequence with constant difference
  • Geometric Progression (GP): Sequence with constant ratio
  • Fibonacci Series: Each number is sum of previous two
  • Factorial Series: Product of all positive integers

Pattern Recognition

  • Square numbers: n²
  • Cube numbers: n³
  • Triangular numbers
  • Prime number sequences

Common Operations

  • Generate first n terms of a series
  • Calculate sum of series
  • Find HCF/GCD using loops
  • Find LCM using loops
  • Factor calculations

Mathematical Formulas

Arithmetic Progression

  • nth term: a + (n-1)d
  • Sum: n/2 * (2a + (n-1)d)

Geometric Progression

  • nth term: a * r^(n-1)
  • Sum: a * (r^n - 1) / (r - 1)

Problem-Solving Approach

  1. Identify the Pattern: What sequence or series?
  2. Determine Formula: Mathematical relationship
  3. Implement Loop: Generate terms or calculate sum
  4. Handle Edge Cases: First term, zero, negative numbers

Common Patterns

  • Generate squares: i * i
  • Generate cubes: i i i
  • Calculate factorials: product of 1 to n
  • Find factors: numbers that divide evenly
  • Calculate GCD: largest common divisor

Hands-on Examples

Print Squares from 1 to N

# Take n as input
n = int(input("Enter n: "))

# Print squares
print("Squares from 1 to", n, ":")
for i in range(1, n + 1):
    square = i * i
    print(f"{i}² = {square}")

Iterate from 1 to n, calculate square (i * i) for each number and print.

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Phase 2 - Level 2: Number-based Looping Logic
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Phase 2 - Level 4: Pattern Printing

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