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Grade 10 Math Lab: Proof & Generalization FREE

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Geometric Sequences & Series

50 min Grade 10 Math Lab: Proof & Generalization

Learning Objectives

  • Identify geometric sequences
  • Find common ratio
  • Sum finite and infinite series

Key Concepts

Common Ratio

r = aₙ₊₁/aₙ — constant multiplier between terms

Geometric Series

Sum of terms: S = a₁(1 - rⁿ)/(1 - r)

Theory

**Geometric sequence:** a, ar, ar², ar³, … **nth term:** aₙ = a₁ · r⁽ⁿ⁻¹⁾ **Finite sum:** Sₙ = a₁(1 - rⁿ)/(1 - r) **Infinite sum** (|r| < 1): S = a₁/(1 - r) **Example:** 2, 6, 18, 54… → r = 3

Examples

Sum of infinite series: 8 + 4 + 2 + 1 + …

Solution: a₁=8, r=½. S = 8/(1-½) = 16