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1. Prayer

2. Attendance Checking

3. To have a classroom with PEACE and HARMONY… Just always remember… LOVE, CARE, RESPECT and SYMPATHY…

4. Review: What was our lesson yesterday? Finding the nth term of an arithmetic sequence using the general term.

5. Answer the following: 1. Find the 8 th term of the sequence, 5, 10, 15,… Answer: 40 2. Find the 15 th of an arithmetic sequence -9, -6, -3, 0, 3,… Answer: 36

6. Drill/Recall Basic Concepts in Math 1. Give the first 6 odd numbers. (Elementary Math) Answer: 1, 3, 5, 7, 9, 11 2. Give the sum of the first 6 odd numbers. Answer: 36

7. Drill: 3. Give the first 5 perfect square numbers. ( Grade 8/9 Math) Answer: 1, 4, 9, 16, 25 4. Give the sum of the first 5 perfect square numbers. Answer: 55

8. Give the sum of the first 5 perfect square numbers. Give the sum of the first 6 odd numbers. What you’ve done are examples of an ARITHMETIC SERIES. sum sum

9. ARITHMETIC SERIES

10. Objectives: 1. Define an arithmetic series. 2. Find the sum of the terms of an a arithmetic sequence given the first term (a 1 ) and the last term (a n ) . 3. Demonstrate the importance of an arithmetic series in real life especially in predicting outcomes.

11. SERIES ARITHMETIC came from the Greek word " arithmos ", meaning numbers. in English, it is a noun in which similar things are placed in order or happening one after another.

12. ARITHMETIC SERIES means the sum of the terms of an arithmetic sequence.

13. Suppose there are 7 seats in front of the theater. Each successive row contains two more seats than the previous row. Theater Have you been to a theater in a mall? What have you noticed about the way the seats are arranged?

14. Questions: 1. What pattern do the seats in the arena make? Adding 2 seats in the previous row 2. How many seats are there in the next 4 rows? 15 seats 3. Can you expect this pattern to continue infinitely? Explain.

15. Questions: 4. If there are 15 rows, how many seats are there in the last row of a circular arena? 35 seats 5. What is the total number of seats in a theater? 315 seats

16. Solution: a n = a 1 + (n – 1)d a 1 = 7 d=2 n=15 a 18 = 7 + (15 – 1)2 a 18 = 7 + (14)2 a 18 = 7 + 28 a 18 = 35

17. Carl Friedrich Gauss S n = (a 1 + a n ) n 2 where: a 1 n (number of terms ) ( first term ) a n ( nth term )

18. Solution: S n = a 1 = 7 a n = a 15 = 35 n 2 n= 15 S 15 = 15 2 S 15 = 15 2 S 7 = 15 2 21 S 7 = 315 1 ( 42 ) (a 1 + a n ) ( 7 + 35 ) ( 42 )

19. Other example: Find the sum of all even numbers from 1 to 50. a 1 = 2 a n = a 25 = 50 n=25 Given: Solution: S n = (a 1 + a n ) n 2

20. S n = (a 1 + a n ) n 2 S 25 = (2 + 50 ) 25 2 S 25 = (52) 25 2 S 25 = (52) 25 2 26 1 S 25 = 650

21. Check the answer using the formula of the sum of the first 6 odd numbers. Answer: 36 By Pair:

22. There GROUP ACTIVITY Title: “Christmas is on the air.”

23. How did you find your activity? Did you learn from it?

24. Aside from the given examples, can you cite other real-life situations wherein arithmetic series is applicable?

25. In TLE, in fashion and accessories you can determine the total number of beads and the cost in your project if you have patterns and sequences. In Business, the business can make a projection on his income based on the outcomes, and he can make decisions whether he will continue with that kind of business.

26. Synthesis: * What is an arithmetic series? * How will you find the sum of an arithmetic sequence given the first term and the last term? * How can outcomes in real-life problems be predicted?

27. Evaluation: 1 . Find the arithmetic series of 3, 6, 9, 12, 15 . Write the given and show your solution. 2. Find the sum of an arithmetic sequence given the following: a 1 = 2 a n =a 8 = 23

28. Assignment: Karen is making an ice water for her customers in her Sari-Sari Store. Before she put it in a freezer she piled it up in a tray with 7 pieces at the bottom layer. She continued making it until she placed 1 piece on the last layer. What is the total number of ice water does Karen made?

29. Solution: S n = (a 1 + a n ) a 1 = 7 a n = a 7 = 1 n 2 n= 7 S 7 = ( 7 + 1 ) 7 2 S 7 = ( 8 ) 7 2 S 7 = ( 8 ) 7 2 4 S 7 = 28 ice waters

30. 28 ice waters

31. Assignment: Think of day-to-day patterns in natural phenomenon that you observed and experienced. Take pictures of them. Add a caption describing the pattern and send it to my messenger.