1 / 12

Warm-Up Question

Warm-Up Question. Find next three numbers of each list of numbers by identifying the pattern. 1, 2, 3, 4, … 2, 4, 6, 8, … 5, 8, 11, 14, … 14, 10, 6, 2, … 2, 4, 8, 16, … 27, 9, 3, 1, … 1, 1, 2, 3, 5, 8, … 1, 3, 7, 15, 31, …. Sequences and Series. Definition of Sequences and Series.

whitley
Download Presentation

Warm-Up Question

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 Question Find next three numbers of each list of numbers by identifying the pattern. 1, 2, 3, 4, … 2, 4, 6, 8, … 5, 8, 11, 14, … 14, 10, 6, 2, … 2, 4, 8, 16, … 27, 9, 3, 1, … 1, 1, 2, 3, 5, 8, … 1, 3, 7, 15, 31, …

  2. Sequences and Series Definition of Sequences and Series

  3. Definition of Sequences Lesson: P.434 Sequence is a function whose domain is a set of consecutive integers starting with 1 unless specified. The values in the range are called the terms of the sequence. Domain: 1 2 3 4 5 6 … n Position of each term Range: Terms of the sequence Examples) 1 2 3 4 5 6 … 100 1 2 3 4 5 6 … 100 1 2 3 4 5 6 … 100 2 4 6 8 10 12 … 200

  4. Terms of sequences Lesson: P.434 Write the first four terms of each sequence. Required Practice: P.434 G.P. 1, 2, 3 Additional Practice: P.438 7, 9, 11, 13

  5. Rules of Sequences Lesson: P.435 Describe the pattern, write the next term, and write a rule for the nth term of each sequence. a) -1, -8, -27, -64 b) 0, 2, 6, 12 Required Practice: P.438 15, 16 Additional Practice: P.438 19, 20

  6. Warm-Up Question (9C) Describe the pattern, write the next term, and write a rule for the nth term of each sequence. 1, 3, 5, 7, 9, … 4, 7, 10, 13, 16, … 5, 1, -3, -7, -11, … 13, 11, 9, 7, 5, …

  7. Warm-Up Question (9AB) Calculate each sum. 1+ 2 = ? 1 + 2 + 3 = ? 1 + 2 + 3 + 4 = ? 1 + 2 + 3 + 4 + 5 = ? 1 + 2 + 3 + 4 + 5 + … + 99 + 100 = ? 2 + 4 = ? 2 + 4 + 6 = ? 2 + 4 + 6 + 8 = ? 2 + 4 + 6 + 8 + 10 = ? 2 + 4 + 6 + 8 + 10 + … + 98 + 100 = ?

  8. Definition of Series Lesson: P.434 When the terms of a sequence are added together, the resulting expression is a series. Sequence: 1 2 3 4 5 6 … n 2 4 6 8 10 12 … n 1 + 2 + 3 + 4 + 5 + 6 + … + n 2 + 4 + 6 + 8 + 10 + 12 + … + n Series:1 3 6 10 15 21 ... 2 6 12 20 30 32 …

  9. Summation Notation Lesson: P.436 Summation notation is often used to write a series. 4: Upper limit of summation 2i: Rule for each term. ∑: Greek letter Sigma to notate summation = 2 + 4 + 6 + 8 1: Lower limit of summation i: Index of summation Ex) Write the series using summation notation. a. 25 + 50 + 75 + … + 250 b. Required Practice: P.436 6, 7, 8, 9 Additional Practice: P.438 39, 40, 43

  10. Sum of a Series Lesson: P.437 Find the sum of the series Required Practice: P.437G.P. 10, 11 Additional Practice: P.439 45, 47, 49

  11. Formula for Special Series Lesson: P.437 Sum of n terms of 1 Sum of first n positive integers Sum of squares of first n positive integers Ex) Find the sum of the series Required Practice: P.437G.P. 12, 13 Additional Practice: P. 439 53, 55, 56

  12. Homework Assignment

More Related