5. Arithmetic sequence.pptx gggggggggggggggg

aaaaaaaaaaaaaaaaaaa

1. Arithmetic sequence Mr. rosilito e. gonzales

2. objectives Illustrate an arithmetic sequence Identify the patterns generated by arithmetic sequence Determine the nth term of an arithmetic sequence Find the missing term, common difference, and number of terms in an arithmetic sequence

3. Answer to the assignment: 1. a n ​ =5n 2 +2n−6 2. a n ​ =2n 2 +4n−3 3. a n = 5n 2 −10n+4 3

4. identifying whether each sequence is linear or not: 2,4,6,8,10 3,6,12,24,48 7,11,15,19,23 5,10,17,26,37 −1,1,3,5,7 4

5. 5 ARITHMETIC SEQUENCE A sequence in which any term is obtained by adding a constant to the preceding term is called an ARITHMETIC SEQUENCE . The constant number is called the common difference denoted by d

6. 6 If we have an arithmetic sequence in the form, a 1 , a 2 , a 3 , a 4 , a 5 , …, a n ,... Where a 1   = first term a 2 = second term and so on…. a n = the  nth term, we have, a 2 -a 1 =d,    a 3 -a 2 =d . How about a 4 -a 3 ?  a 5 -a 4 ? d is the common difference in an arithmetic sequence.

7. 7 What if you are asked to find the nth term of any arithmetic sequence? Let’s have:   a 1 a 2 = a 1 +d a 3 = a 2 +d =  a 1 +d+d = a 1 +2d How about  a 4 ? a 5 ?   do you see any pattern? From these equations, what can you notice between the nth term (n) and the coefficient of the common difference (d)?

8. 8 ARITHMETIC SEQUENCE FORMULA: Where:  

9. ans : 89 ans : 156 ans : -48   2. 2, 9, 16, 23, …   3. 64, 56, 48, 40, …                                       CASE I: Find the required term ( nth term ) Find the required term for each sequence: FORMULA:  

10. CASE I: Find the required term ( nth term ) Find the required term for each sequence: ans : 97 ans : -76 ans : 296 FORMULA:     2. 22, 15, 8, 1, -6 …   3. 6, 16, 26, 36, …                                      

11. 11 CASE II: Find the number of term ( n=?) FORMULA:   FOR :     Find to what term the given last term of the sequence is. 1. 4, 9, 14, 19, …, 109         ans : 22nd

12. 12 FORMULA:   FOR :     Find to what term the given last term of the sequence is. 2. 2, 9, 16, 23, …, 79         ans : 12th CASE II: Find the number of term ( n=?)

13. 13 CASE III: Find the common difference ( d ) FORMULA:   FOR :     Find the common difference given the and :   1. Find the common difference of the sequence whose and           ans : 4

14. 14 FORMULA:   FOR :     Find the common difference given the and :   2. Find the common difference of the sequence whose and           ans : 4 CASE III: Find the common difference ( d )

15. 15 Let’s do It!! Answer the following : 1. Find the 15 th term of Arithmetic sequence -4, 5, 14, 23,… ans : 122 2. In the Arithmetic sequence from #1, to what term is 176 ? ans : 21st 3. Find the common difference of the sequence whose and ans : -6  

16. 16 Generalization: A sequence in which any term is obtained by adding a constant to the preceding term is called an ARITHMETIC SEQUENCE . To find the nth term ( ) of Arithmetic sequence use: To find the number of term ( n ) of Arithmetic sequence use: To find the common difference ( d ) of arithmetic sequence:  

17. A. Find the term indicated in each of the following arithmetic sequence. 1) 3, 6, 9, 12,...   20th term 2) -2, -4, -6, -8,...   25th term 3) 91, 84, 77, 70,...   10th term B. In the arithmetic sequence -3, 0, 3, 6... which term (n) equals 138 ? C. Solve for the common difference. 1) Find the common difference of a sequence with a1=-9 and  a5=6 . 2) Find the common difference of a sequence with a12=5 and  a17=25 . ASSIGNMENT