Strengthened SHS Curriculum - General Mathematics-Sequences & Series.pptx

Strengthened SHS Curriculum - General Mathematics Lesson 3

1. 25, 50, 75, 100, 125, ... 2, 3, 4, 5, 6, ... 4, 7, 10, 13, 16, ... 3, 5, 6, 7, 8, ... 4, 7, 10, 13, 16, ... 2, 10, 50, 250, 1250 ... -2, 10, -50, 250, -1250 ... 2, 10, 50, 250, 1250 ... 9, 18, 27, 36, 45, .... -6, -8, -10, -12, -14, ... 10, 20, 30, 40, 50, ... 10, 20, 30, 40, 50, ... 10, 20, 30, 40, 50, ... 3, 5, 6, 7, 8, ... 4, 7, 10, 13, 16, ... 7, 21, 63, 189, 567, .... 1.5, 3, 4.5, 6, 7.5, .... 11, 22, 33, 44, 55, ... 2.25, 4.5, 9, 18, 36, ... 4, 8, 16, 32,... 4, 7, 10, 13, 16, ... 7, 21, 63, 189, 567, .... 2, 3, 4, 5, 6, ... 4, 7, 10, 13, 16, ... 4, 8, 16, 32,... 3, 5, 6, 7, 8, ... 4, 7, 10, 13, 16, ... 2, 10, 50, 250, 1250 ... 3, 5, 6, 7, 8, ... 2, 10, 50, 250, 1250 ... 2, 3, 4, 5, 6, ... 2, 10, 50, 250, 1250 ... 3, 5, 6, 7, 8, ... 4, 7, 10, 13, 16, ... -2, 10, -50, 250, -1250 ... 10, 20, 30, 40, 50, ... 7, 21, 63, 189, 567, .... 2, 3, 4, 5, 6, ... Sequences & Series

2. Activity – Spin the Wheel of Names Spin the wheel with the students’ names on it. Let the picked students answer the given question on the board.

3. Activity – Spin the Wheel of Names 1) 2, 4, 6, _ Give the next missing term. Give the rule.

4. Activity – Spin the Wheel of Names 2) 1, 1, 2, 3, _ Give the next missing term. Give the rule.

5. Activity – Spin the Wheel of Names 3) 100, 90, 80, _ Give the next missing term. Give the rule.

6. Activity – Spin the Wheel of Names 4) Square tile patterns: 1 tile, 4 tiles, 9 tiles, _ Give the next missing term. Give the rule.

7. Activity – Spin the Wheel of Names 5) 3, 6, 9, 12, _ Give the next missing term. Give the rule. 3 + 6 + 9 + 12 + 15 = _

8. Activity – Spin the Wheel of Names 6) 0.1, 0.2, 0.3, _ Give the next missing term. Give the rule. 0.1 + 0.2 + 0.3 + 0.4 = _

9. Key Terms and Definitions Series - the sum of the terms of a sequence. Example: For the sequence 1, 3, 5, the series is 1 + 3 + 5 = 9

10. Key Terms and Definitions Finite Series - a series with a definite number of terms. Example: 2 + 4 + 6 + 8 (only 4 terms)

11. Key Terms and Definitions Infinite Series - a series that continues without end. Example: 1 + ½ + ¼ + 1/8 + …

12. Key Terms and Definitions The n th term of a sequence is usually denoted by a n Partial Sum ( S n ) - the sum of the first (n) terms of a sequence.

13. Key Terms and Definitions If the nth term of the sequence is a n , then S n = a 1 + a 2 + a 3 +...+ a n Example: In the sequence, 1, 3, 5, 7, 9, ..., S 4 = 1 + 3 + 5 + 7 = 16 S n is the nth term of the series

14. Key Terms and Definitions Sigma Notation (∑) - a shorthand symbol used to express a series. To write a 1 + a 2 + a 3 + … + a n in sigma notation:

15. Key Terms and Definitions In general, (expression in terms of a n ) Example: 1 + 2 + 3 + 4 + 5 in sigma notation is

16. Let’s Practice ( Saving Up Smartly – A Real-Life Application of Sequences ) Scenario: A student wants to build a personal savings fund. They commit to saving ₱50.00 in the first week and increase the amount they save by ₱15.00 each week. Week 1: ₱50.00 Week 2: ₱65.00 Week 3: ₱80.00

17. Let’s Practice ( Saving Up Smartly – A Real-Life Application of Sequences ) Question: 1) How much will the student save in Week 10? 2) How much will the student have saved in total after 10 weeks?

18. Let’s Practice ( Saving Up Smartly – A Real-Life Application of Sequences ) Question: 3) If the student’s goal is to save ₱1,500.00, in how many weeks will the goal be met or exceeded? 4) How can this type of savings plan help in achieving financial goals such as buying a gadget, funding a project, or starting a small business?

19. Evaluating Learning 1) Which of the following best describes a series? A) A sum of numbers in a pattern B) A list of numbers in a specific order C) A variable expression with a pattern D) A formula for a term

20. Evaluating Learning 2) Which of the following is a series? A) 2, 4, 6, 8 B) 3, 6, 9, 12 C) 2 + 4 + 6 + 8 D) 1, 3, 5, 7

21. Evaluating Learning 3) What does the sigma symbol (∑) represent in mathematics? A) A product B) A term C) A square root D) A sum

22. Evaluating Learning 4) What is the sigma notation of the series 5 + 10 + 15 + 20? A) C) B) D)  

23. Evaluating Learning 5) What is the sigma notation for 1 + 3 + 9 + 27? A) C) B) D )  

24. Answers Key 1) A 2) C 3) D 4) A 5) B