Mathematics Grade 10 - Lecture by Ma'am Melanie

Introduction

• Teacher: Melanie M. Helzano
• School: Nabunturan National Comprehensive High School
• Subject: Mathematics, Grade 10
• Topic: Sequences (Arithmetic and Geometric)

Key Points

Arithmetic Sequences

• Definition: A sequence where each term is obtained by adding a fixed number to the previous term
• Example: 5, 10, 15, 20, 15, 13, 11, 9
• Note: This sequence has a fixed pattern

Ratios

• Concept: Comparison of two numbers by division
• Examples:
  • (\frac{2}{4} = \frac{1}{2})
  • (\frac{2}{8} = \frac{1}{4})
  • (\frac{9}{3} = 3)
  • (\frac{7}{49} = \frac{1}{7})
  • (\frac{a^3}{a^4} = \frac{1}{a})
• Importance: Understanding ratios helps in understanding sequences

Geometric Sequences

• Definition: A sequence where each term is obtained by multiplying the previous term by a fixed non-zero constant (common ratio)
• Activity: Paper folding to illustrate geometric sequences
  • Starting area: 64 square inches
  • Steps: Fold corners, measure, repeat
  • Results: 32, 16, 8, 4, 2, 1
• Common Ratio Calculation:
  • (\frac{16}{32} = \frac{1}{2})
  • (\frac{8}{16} = \frac{1}{2})
  • (\frac{4}{8} = \frac{1}{2})
  • Common ratio: (\frac{1}{2})
• Example:
  • Sequence: 2, 6, 18, 54
  • Common ratio: 3

Activities

Missing in Action

1. Sequence: 3, 12, 48 - Next term?
2. Sequence: 12, 36, 108 - First term?
3. Sequence: 3x^2, 3x^6, 3x^8 - Second term?
4. Sequence: (\frac{1}{3}, \frac{1}{9}, \frac{1}{27}) - Fourth term?

Identifying Sequences

• Identify the sequences:
  • A: 125, 25, 5, 1 - Geometric, common ratio: (\frac{1}{5})
  • B: 50, 35, 20, 5 - Arithmetic, common difference: -15
  • C: (\frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}) - Arithmetic, common difference: (\frac{1}{4})
  • D: 5, -10, 20, -40 - Geometric, common ratio: -2

Summary

• Geometric Sequence:
  • Defined by a common ratio
  • Examples: Sequences used in predicting COVID-19 cases
• Arithmetic Sequence:
  • Defined by a common difference
• Importance: Distinguishing between geometric and arithmetic sequences and their applications in real life

Conclusion

• Reminders:
  • Wash your hands
  • Maintain social distancing
  • Stay healthy (physically and mentally)
  • Stay home and stay safe
• Sign-off: "Dito sa TV Eskwela, sa pag-aaral, sama-sama."