Finite geometric Series for grade10.pptx

finite geometric series lesson

1. Geometric Series Finite Geometric Series

2. Learning Objectives Defines finite geometric series. Finds the sum of a finite geometric sequence if: r ≠ 1 r = 1 r = -1 & n is even r = -1 & n is odd

3. Gabriel wants to spend his 12-day Christmas break productively by working in “Alamat Restaurant” located at Picnic Grove. The manager offers 2 salary scheme:

4. 1.) Php100 per day 2. or Php1 on the 1st day,Php 2 on the 2nd day, Php4 on the 3rd day and double the salary each day until the 12th day. If you were Gabriel, which salary scheme are you going to accept? Why?

5. After 12 days, how much will Gabriel receive?

6. Speed Quiz

7. Find the sum of the first five terms of the following geometric sequence

8. 3 , 12 , 48 3+12+48+192+768 = 1023

9. 1 , 6 , 36 1555

10. 54 , 18 , 6 242/3 or 80 2/3

11. 7 , 14 , 28 7+14+28+56+112=217

12. 7 , 14 , 28 Challenge: Find the sum up to 20 terms…

13. .Example 1: Find the sum of the first five terms of the sequence 7, 14, 28

14. Example 2: Find the sum of the first seven terms of geometric sequence whose first term is 3 and r = 4

15. Tips to remember

16. 2, -2, 2, - 2, 2, -, 2, 2 When r = -1 and n is even then, S 8 = = 0  

17. 2, -2, 2, - 2, 2, -, 2, 2, -2 2. When r = -1 and n is odd then, S 7 = = 2 (value of a 1 )  

18. 2, 2, 2, 2, 2, 2, 2, 2 3. When r = 1, then S 8 = na 1 = 8(2) = 16

19. Lets Practice

20. 2 , 6 , 1 8,… Find S6

21. 3 , 12, 48,… Find S7

22. 3 . 25 Terms of 3, 3, 3, …. S25 = 3*75

23. 4. 100 Terms of -6, 6, -6, 6,-6, 6 … S100 = 0

24. 5 . 7 Terms of 27, 9, 3 ….

25. Activity Time