1 / 19

Warm Up Find the next two numbers in the pattern, using the simplest rule you can find.

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.

olesia
Download Presentation

Warm Up Find the next two numbers in the pattern, using the simplest rule you can find.

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 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

  2. Learn to find terms in an arithmetic sequence.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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

  17. 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

  18. 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

  19. Using Arithmetic Sequence Formula to write a linear equation. Find the value of y when x = 1: -2 Find the common difference: -4 Use an = a1 + (n – 1)d: rewrite an = y, a1 = value of y when x = 1, n = x y =-2 + (x – 1)(-4) = -2 – 4x + 5 Simplify: y = -4x + 2

More Related