Lesson-4.4_Geometric-Series. general Mathematics.(1).pptx

General Mathematics Quarter 1, First Semester, SHS

1. GEOMETRIC SERIES

2. SPECIFIC OBJECTIVES (SMART) 1 Define geometric series 2 Illustrate geometric series 3 Solving problems involving geometric series

3. ACTIVATE PRIOR KNOWLEDGE Think of an examples of sequences or patterns they have encountered in real life.

4. ACQUIRE KNOWLEDGE A geometric series is the sum of finite or infinite terms of a geometric sequence. The sequence is of the form {a, ar, ar², ar³, …….} where, a is the first term, and r is the "common ratio".

5. 2 TYPES OF GEOMETRIC SERIES Finite – ending Example: 2+4+8+10 Infinite – never ending Example: 2+4+8+10+…10 th term

6. FINITE GEOMETRIC SERIES Formula 1: The sum formula of a finite geometric series a + ar + ar² + ar³ + ... + a r^(n-1) is where, a₁ is the first term r is the common ratio, r=   n is the number of terms

7. EXAMPLE: FINITE SERIES Find the sum of the geometric series: 2+4+8+16 Identify the values a₁ = 2 r = 2 n = 4 Apply the formula Calculate the sum

8. INFINITE GEOMETRIC SERIES Formula 2: The sum formula of an infinite geometric series a + ar + ar² + ar³ + ... is where, a₁ is the first term r is the common ratio every two successive terms  

9. EXAMPLE: INFINITE SERIES Find the sum of the infinite geometric series: 4 + 2 + 1 + 0.5 +… Identify the values a₁ = 4 r = 1/2 Apply the formula Calculate the sum

10. APPLY KNOWLEDGE Think-pair-share activity: Solve the given problem with your seatmate. Problem: John saves ₱100 in the first month. Every month, he saves twice as much as the previous month. How much money will John have saved after 4 months? 100 + 200 + 400 + 800 a₁ = 100 r = 2 n = 4

11. ASSESS KNOWLEDGE Quiz Problem: Lily deposits ₱50 in the first week. Each week, she deposits 3 times as much as the previous week. We want to find the total amount she deposits after 8 weeks. Solution: a₁ = 50 r = 3 n = 8 Let the students rate their learning out of 10.