1 / 35

Warm Up

Warm Up . Write the explicit and recursive formula 3, 7, 11, 15…. 2. 6, 3, 1.5, 0.75… Find the 1 st 5 terms: t 1 = 4, t n = t n-1 +5 4. t n =4(2) n-1 Find the 10 th term: 5. t 1 = 3, t n = 3t n-1 6. t n =2 + 4n. Arithmetic Sequences and Series. Sequences. Series.

gregg
Download Presentation

Warm Up

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. Warm Up Write the explicit and recursive formula • 3, 7, 11, 15…. 2. 6, 3, 1.5, 0.75… Find the 1st 5 terms: • t1= 4, tn= tn-1+5 4. tn=4(2)n-1 Find the 10th term: 5. t1= 3, tn= 3tn-1 6. tn=2 + 4n

  2. Arithmetic Sequences and Series

  3. Sequences Series “Indicated sum” List with commas 3, 8, 13, 18 3 + 8 + 13 + 18

  4. Arithmetic Sequences

  5. An Arithmetic Sequence is definedas a sequence in which there is a common difference between consecutive terms.

  6. Which of the following sequences are arithmetic? Identify the common difference. YES YES NO NO YES

  7. The common difference is always the difference between any term and the term that proceeds that term. Common Difference = 5

  8. The general form of an ARITHMETIC sequence. First Term: Second Term: Third Term: Fourth Term: Fifth Term: nth Term:

  9. Formula for the nth term of an ARITHMETIC sequence. If we know any three of these we ought to be able to find the fourth.

  10. Given: Find: IDENTIFY SOLVE

  11. Given: Find: What term number is -169? IDENTIFY SOLVE

  12. Find: Given: What’s the real question? The Difference IDENTIFY SOLVE

  13. Find: Given: IDENTIFY SOLVE

  14. Arithmetic Series

  15. What is the sum of this series?

  16. 50 Terms 71 + (-27) Each sum is the same. What is the SUM of these terms? Written 1st to last. Written last to 1st. Add Down

  17. In General . . .

  18. Find the sum of the terms of this arithmetic series.

  19. Find the sum of the terms of this arithmetic series. What term is -5?

  20. Alternate formula for the sum of an Arithmetic Series.

  21. Find the sum of this series It is not convenient to find the last term.

  22. Your Turn

  23. Vocabulary of Sequences (Universal)

  24. Given an arithmetic sequence with x 38 15 NA -3 X = 80

  25. -19 353 ?? 63 x 6

  26. 1.5 x 16 NA 0.5 Try this one:

  27. 9 633 x NA 24 X = 27

  28. -6 20 29 NA x

  29. The two arithmetic means are –1 and 2, since –4, -1, 2, 5 forms an arithmetic sequence Find two arithmetic means between –4 and 5 -4, ____, ____, 5 -4 5 4 NA x

  30. The three arithmetic means are 7/4, 10/4, and 13/4 since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequence Find three arithmetic means between 1 and 4 1, ____, ____, ____, 4 1 4 5 NA x

  31. Find n for the series in which 5 y x 440 3 Graph on positive window X = 16

  32. The sum of the first n terms of an infinite sequence is called the nth partial sum. Example: The nth Partial Sum

  33. Example 6. Find the 150th partial sum of the arithmetic sequence, 5, 16, 27, 38, 49, …

  34. Example 7. An auditorium has 20 rows of seats. There are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. How many seats are there in all 20 rows?

  35. Example 8. A small business sells $10,000 worth of sports memorabilia during its first year. The owner of the business has set a goal of increasing annual sales by $7500 each year for 19 years. Assuming that the goal is met, find the total sales during the first 20 years this business is in operation. So the total sales for the first 2o years is $1,625,000

More Related