GRADE 10 arithmetic sequence power.pptx

one of the types of sequences

1. RECALL DETERMINE WHETHER EACH SEQUENCE IS ARITHMETIC OR NOT. IF IT IS, FIND THE COMMON DIFFERENCE AND GIVE THE NEXT TERM/ ARITHMETIC OR NOT ARITHMETIC? IF YES, FIND The d and the next terme d Next term 1. 7, 10, 13, 16,… 2. 9, 11, 13, 15, … 3. 4, 12, 36, 108,… 4. 20, 6, 3, 1 ½, … 5. 3, 5, 8, 12, 17, … 6. 2, -2, -6, -10

2. ARITHMETIC OR NOT ARITHMETIC? IF YES, FIND The d and the next terme d Next term 1. 7, 10, 13, 16,… ARITHMETIC 3 19 2. 9, 11, 13, 15, … ARITHMETIC 2 17 3. 4, 12, 36, 108,… NOT ARITHMETIC 4. 20, 6, 3, 1 ½, … NOT ARITHMETIC 5. 3, 5, 8, 12, 17, … NOT ARITHMETIC 6. 2, -2, -6, -10 ARITHMETIC -4 -14

3. How do you find any term in this sequence? To find any term in an arithmetic sequence, use the formula a n = a 1 + (n – 1)d where d is the common difference.

4. Vocabulary of Sequences (Universal)

5. Examples: Find the 14 th term of the arithmetic sequence 4, 7, 10, 13,……

6. Try this one: 1.5 16 a 16 0.5 a 16 = 1.5 + ( 16 - 1) (0.5) a 16 = 1.5 + (15)(0.5) a 16 = 1.5+7.5 a 16 = 9

7. Months Cost ($) 1 75,000 2 90,000 3 105,000 4 120,000 The table shows typical costs for a construction company to rent a crane for one, two, three, or four months. Assuming that the arithmetic sequence continues, how much would it cost to rent the crane for twelve months? 75,000 12 a 12 15,000 a 12 = 75,000 + ( 12 - 1) (15,000) a 12 = 75,000 + (11)(15,000) a 12 = 75,000+165,000 a 12 = $240,000

8. Examples: In the arithmetic sequence 4,7,10,13,…, which term has a value of 301?

9. 9 n 633 24 Try this one: 633 = 9 + ( n - 1) (24) 633 = 9 + 24n - 24 633 = 24n – 15 648 = 24n n = 27

10. Given an arithmetic sequence with a 1 15 38 -3 38 = a 1 + ( 15 - 1) (-3) 38 = a 1 + (14)(-3) 38 = a 1 - 42 a 1 = 80

11. -6 29 20 NA d 20 = -6 + ( 29 - 1) (d) 20 = -6 + (28)( d ) 26 = 28 d

12. Write an equation for the n th term of the arithmetic sequence 8, 17, 26, 35, … 8 9 a n = 8 + (n - 1) (9) a n = 8 + 9n - 9 a n = 9n - 1

13. Arithmetic Mean: The terms between any two nonconsecutive terms of an arithmetic sequence. Ex. 19, 30, 41, 52, 63, 74, 85, 96 41, 52, 63 are the Arithmetic Mean between 30 and 74

14. Find two arithmetic means between –4 and 5 -4, ____, ____, 5 -4 4 5 NA d The two arithmetic means are –1 and 2, since –4, -1, 2 , 5 forms an arithmetic sequence 5 = -4 + ( 4 - 1) (d) 5 = -4 + (3)( d ) 9 = (3)( d ) d = 3

15. Find three arithmetic means between 21 and 45 21, ____, ____, ____, 45 21 5 45 NA d The three arithmetic means are 27, 33, and 39 since 21, 27, 33, 39 , 45 forms an arithmetic sequence 45 = 21 + ( 5 - 1) (d) 45 = 21 + (4)( d ) 24 = (4)( d ) d = 6

16. Arithmetic Series: An indicated sum of terms in an arithmetic sequence. Example: Arithmetic Sequence 3, 5, 7, 9, 11, 13 VS Arithmetic Series 3 + 5 + 7 + 9 + 11 + 13

17. 1.WHAT IS THE SUM OF THE FIRST 30 EVEN NUMBERS? 2. WHAT IS SUM OF THE 20 TERMS OF THE SEQUENCE 3, 6, 9,..?