1 / 30

13-1

Terms of Arithmetic Sequences. 13-1. Course 3. Warm Up. Problem of the Day. Lesson Presentation. Terms of Arithmetic Sequences. 13-1. Course 3. Warm Up Find the next two numbers in the pattern, using the simplest rule you can find. 1. 1, 5, 9, 13, . . . 2. 100, 50, 25, 12.5, . . .

dakota
Download Presentation

13-1

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Terms of Arithmetic Sequences 13-1 Course 3 Warm Up Problem of the Day Lesson Presentation

  2. Terms of Arithmetic Sequences 13-1 Course 3 Warm Up Find the next two numbers in the pattern, using the simplest rule you can find. 1.1, 5, 9, 13, . . . 2. 100, 50, 25, 12.5, . . . 3. 80, 87, 94, 101, . . . 4. 3, 9, 7, 13, 11, . . . 17, 21 6.25, 3.125 108, 115 17, 15

  3. Problem of the Day Write the last part of this set of equations so that its graph is the letter W. y = –2x + 4 for 0 x 2 y = 2x – 4 for 2 < x 4 y = –2x + 12 for 4 < x 6 Possible answer: y = 2x – 12 for 6 < x 8

  4. Learn to find terms in an arithmetic sequence.

  5. Caution! You cannot tell if a sequence is arithmetic by looking at a finite number of terms because the next term might not fit the pattern.

  6. Additional Example 1A: Identifying Arithmetic Sequences Determine if the sequence could be arithmetic. If so, give the common difference. 5, 8, 11, 14, 17, . . . The terms increase by 3. 5 8 11 14 17, . . . 3 3 3 3 The sequence could be arithmetic with a common difference of 3.

  7. Additional Example 1B: Identifying Arithmetic Sequences Determine if the sequence could be arithmetic. If so, give the common difference. 1, 3, 6, 10, 15, . . . Find the difference of each term and the term before it. 1 3 6 10 15, . . . 5 4 2 3 The sequence is not arithmetic.

  8. Additional Example 1C: Identifying Arithmetic Sequences Determine if the sequence could be arithmetic. If so, give the common difference. 65, 60, 55, 50, 45, . . . The terms decrease by 5. 65 60 55 50 45, . . . –5 –5 –5 –5 The sequence could be arithmetic with a common difference of –5.

  9. Additional Example 1D: Identifying Arithmetic Sequences Determine if the sequence could be arithmetic. If so, give the common difference. 5.7, 5.8, 5.9, 6, 6.1, . . . The terms increase by 0.1. 5.7 5.8 5.9 6 6.1, . . . 0.1 0.1 0.1 0.1 The sequence could be arithmetic with a common difference of 0.1.

  10. Additional Example 1E: Identifying Arithmetic Sequences Determine if the sequence could be arithmetic. If so, give the common difference. 1, 0, -1, 0, 1, . . . Find the difference of each term and the term before it. 1 0 –1 0 1, . . . 1 1 –1 –1 The sequence is not arithmetic.

  11. Check It Out: Example 1A Determine if the sequence could be arithmetic. If so, give the common difference. 1, 2, 3, 4, 5, . . . The terms increase by 1. 1 2 3 4 5, . . . 1 1 1 1 The sequence could be arithmetic with a common difference of 1.

  12. Check It Out: Example 1B Determine if the sequence could be arithmetic. If so, give the common difference. 1, 3, 7, 8, 12, … Find the difference of each term and the term before it. 1 3 7 8 12, . . . 4 1 2 4 The sequence is not arithmetic.

  13. Check It Out: Example 1C Determine if the sequence could be arithmetic. If so, give the common difference. 11, 22, 33, 44, 55, . . . The terms increase by 11. 11 22 33 44 55, . . . 11 11 11 11 The sequence could be arithmetic with a common difference of 11.

  14. Check It Out: Example 1D Determine if the sequence could be arithmetic. If so, give the common difference. 1, 1, 1, 1, 1, 1, . . . Find the difference of each term and the term before it. 1 1 1 1 1, . . . 0 0 0 0 The sequence could be arithmetic with a common difference of 0.

  15. Check It Out: Example 1E Determine if the sequence could be arithmetic. If so, give the common difference. 2, 4, 6, 8, 9, . . . Find the difference of each term and the term before it. 2 4 6 8 9, . . . 1 2 2 2 The sequence is not arithmetic.

  16. Helpful Hint Subscripts are used to show the positions of terms in the sequence. The first term is a1, “read a sub one,” the second is a2, and so on.

  17. Additional Example 2A: Finding a Given Term of an Arithmetic Sequence Find the given term in the arithmetic sequence. 10th term: 1, 3, 5, 7, . . . an = a1 + (n – 1)d a10 = 1 + (10 – 1)2 a10 = 19

  18. Additional Example 2B: Finding a Given Term of an Arithmetic Sequence Find the given term in the arithmetic sequence. 18th term: 100, 93, 86, 79, . . . an = a1 + (n – 1)d a18 = 100 + (18 – 1)(–7) a18 = -19

  19. Additional Example 2C: Finding a Given Term of an Arithmetic Sequence Find the given term in the arithmetic sequence. 21st term: 25, 25.5, 26, 26.5, . . . an = a1 + (n – 1)d a21 = 25 + (21 – 1)(0.5) a21 = 35

  20. Additional Example 2D: Finding a Given Term of an Arithmetic Sequence Find the given term in the arithmetic sequence. 14th term: a1 = 13, d = 5 an = a1 + (n – 1)d a14 = 13 + (14 – 1)5 a14 = 78

  21. Check it Out: Example 2A Find the given term in the arithmetic sequence. 15th term: 1, 3, 5, 7, . . . an = a1 + (n – 1)d a15 = 1 + (15 – 1)2 a15 = 29

  22. Check It Out: Example 2B Find the given term in the arithmetic sequence. 50th term: 100, 93, 86, 79, . . . an = a1 + (n – 1)d a50 = 100 + (50 – 1)(-7) a50 = –243

  23. Check It Out: Example 2C Find the given term in the arithmetic sequence. 41st term: 25, 25.5, 26, 26.5, . . . an = a1 + (n – 1)d a41 = 25 + (41 – 1)(0.5) a41 = 45

  24. Check It Out: Example 2D Find the given term in the arithmetic sequence. 2nd term: a1 = 13, d = 5 an = a1 + (n – 1)d a2 = 13 + (2 – 1)5 a2 = 18

  25. You can use the formula for the nth term of an arithmetic sequence to solve for other variables.

  26. Additional Example 3: Application The senior class held a bake sale. At the beginning of the sale, there was $20 in the cash box. Each item in the sale cost 50 cents. At the end of the sale, there was $63.50 in the cash box. How many items were sold during the bake sale? Identify the arithmetic sequence: 20.5, 21, 21.5, 22, . . . a1 = 20.5 a1 = 20.5 = money after first sale d = 0.5 d = .50 = common difference an = 63.5 an = 63.5 = money at the end of the sale

  27. Additional Example 3 Continued Let n represent the item number of cookies sold that will earn the class a total of $63.50. Use the formula for arithmetic sequences. an = a1 + (n – 1) d 63.5 = 20.5 + (n – 1)(0.5) Solve for n. Distributive Property. 63.5 = 20.5 + 0.5n – 0.5 63.5 = 20 + 0.5n Combine like terms. 43.5 = 0.5n Subtract 20 from both sides. Divide both sides by 0.5. 87 = n During the bake sale, 87 items are sold in order for the cash box to contain $63.50.

  28. Check It Out: Example 3 Johnnie is selling pencils for student council. At the beginning of the day, there was $10 in his money bag. Each pencil costs 25 cents. At the end of the day, he had $40 in his money bag. How many pencils were sold during the day? Identify the arithmetic sequence: 10.25, 10.5, 10.75, 11, … a1 = 10.25 a1 = 10.25 = money after first sale d = 0.25 d = .25 = common difference an = 40 an = 40 = money at the end of the sale

  29. Check It Out: Example 3 Continued Let n represent the number of pencils in which he will have $40 in his money bag. Use the formula for arithmetic sequences. an = a1 + (n – 1)d 40 = 10.25 + (n – 1)(0.25) Solve for n. 40 = 10.25 + 0.25n – 0.25 Distributive Property. Combine like terms. 40 = 10 + 0.25n Subtract 10 from both sides. 30 = 0.25n 120 = n Divide both sides by 0.25. 120 pencils are sold in order for his money bag to contain $40.

  30. 27 5 3 7 , or 6.75 4 4 2 4 Lesson Quiz Determine if each sequence could be arithmetic. If so, give the common difference. 1. 42, 49, 56, 63, 70, . . . 2. 1, 2, 4, 8, 16, 32, . . . Find the given term in each arithmetic sequence. 3. 15th term: a1 = 7, d = 5 4. 24th term: 1, , , , 2 5. 52nd term: a1 = 14.2; d = –1.2 yes; 7 no 77 –47

More Related