aritmetic vs. geometric

June 27

1. Still remember this? 3 T he sitting arrangement done last year when you took the NCAE. There were 30 students in each room. The table 1 shows that the number of students varies directly as the number of rooms or as the number of rooms increases, the number of students also increases. Can you guess the number of students when there are 12 rooms used? Table 1 is an example of Arithmetic Sequence.

2. 5 Suppose that the number of a certain bacteria grows as shown in table 2 below. At the start, there are only 1, 000 bacteria and after 1 hour the number of bacteria is doubled. It is consistent that based from the observation, the number of bacteria is always doubled every hour. Can you tell the number of bacteria after 7 hours? 10 hours? Table 2 is an example of Geometric Sequence

3. 6 1. What have you observed about the differences of the arithmetic and geometric sequence?

4. 7 2 . Can you tell the number of students who took the NCAE if there were 12 rooms used during the examination?

5. 8 3 . How many bacteria would there be after 7 hours if we consider the data in table 2?

6. 9 4. Can you define arithmetic sequence? Geometric sequence?

7. 10 Let them know!

8. 11 State whether each of the following sequences is arithmetic or geometric. Write “-” if it is arithmetic and “ ” if geometric.  

9. 12 Ready?

10. 13   -

11. 14    

12. 15    

13. 16    

14. 17    

15. 18   -

16. 19 How do you find doing the activity?

17. 20 What is the most important characteristics that you should remember in identifying arithmetic or geometric sequence?

18. 21 What kind of sequence is  

19. 22 What kind of sequence is 2, 6, 18, 54, 162, … ?

20. 23 What kind of sequence is 2, 6, 18, 54, 162, … ?

21. 24 Example 1. Examine the sequence Step 1. Subtract the second term by the first term (d = right term – left term) Step 2. Check if the difference between the third term and the second term is the same with step 1. (d = right term – left term) Step 3. Therefore, the sequence has a common difference,  

22. 25 Example 2 . Examine the sequence 2, 6, 18, 54, 162 … Step 1. Divide the second term by the first term (r = right term divided by the left term) Step 2. Check the result if the same operation is applicable to get the third term. (r = right term divided by the left term) Step 3. Therefore, the sequence has a common ratio, r  

23. 26 Exercise # 1. __ State whether each of the following sequences is arithmetic or geometric : 1. 3, 9, 27, 81, 243 … 2. 7, 21, 63, 189, 567 … 3. 7, 14, 21, 28, 35 … 4. 5, 25, 45, 65, 85 … 5. 2, 8, 32, 128, 512… 6.   7 . 8 . 9 . 10.  

24. 27 Arithmetic Sequence is a sequence where each term after the first is obtained by adding the same constant, called the common difference. Common Difference is a constant added to each term of an arithmetic sequence to obtain the next term of the sequence. Geometric Sequence is a sequence where each term after the first is obtained by multiplying the preceding term by a nonzero constant called the common ratio. Common Ratio is a constant multiplied to each term of a geometric sequence to obtain the next term of the sequence.

25. 28 Quiz # 1. __ 1. Define arithmetic sequence and geometric sequence.

26. 29 2 . What is common difference? Common ratio? State whether the given sequence is an arithmetic or geometric ? a. b. c.