1 / 17

9-1

9-1. Geometric Sequences. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 1. Holt Algebra 1. Warm Up 02/14/17 Find the value of each expression. 1. 2 5. 2. 2 –5. 3. –3 4. 4. (–3) 4. 5. (0.2) 3. 6. 7(–4) 2. 7. 8. 12(–0.4) 3. Essential Questions.

albertblair
Download Presentation

9-1

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. 9-1 Geometric Sequences Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

  2. Warm Up 02/14/17 Find the value of each expression. 1. 25 2. 2–5 3. –34 4. (–3)4 5. (0.2)3 6. 7(–4)2 7. 8. 12(–0.4)3

  3. Essential Questions 1. How do you recognize and extend geometric sequences? 2. How do you find the nth term of a geometric sequence? Exponential Function y = a(b)^x

  4. In a Geometric sequence, the ratio of successive terms is the same number r, called the common ratio (constantly multiplied)

  5. Example: Extending Geometric Sequences 1, 4, 16, 64,… Step 1 Find the value of r by dividing each term by the one before it. 1 4 16 64 The value of r is 4.

  6. 4 4 4 Example: continued Find the next three terms in the geometric sequence. 1, 4, 16, 64,… Step 2 Multiply each term by 4 to find the next three terms. 64 256 1024 4096 The next three terms are 256, 1024, and 4096.

  7. Helpful Hint When the terms in a geometric sequence alternate between positive and negative, the value of r is negative.

  8. – The value of r is . Example Find the next three terms in the geometric sequence. Step 1 Find the value of r by dividing each term by the one before it.

  9. Step 2 Multiply each term by to find the next three terms. The next three terms are Example Continued

  10. Example Find the next three terms in the geometric sequence. 5, –10, 20,–40,… 5 –10 20 –40 The value of r is –2.

  11. Example Continued 5, –10, 20,–40,… The next three terms are 80, –160, and 320.

  12. nth term 1st term Common ratio If the first term of a geometric sequence is a1, the nth term is an , and the common ratio is r, then an=a1rn–1

  13. Example The first term of a geometric sequence is 500, and the common ratio is 0.2. What is the 7th term of the sequence? an = a1rn–1 a7 = 500(0.2)7–1 = 500(0.2)6 = 0.032 The 7th term of the sequence is 0.032.

  14. Example For a geometric sequence, a1 = 5, and r = 2. Find the 6th term of the sequence. an = a1rn–1 a6 = 5(2)6–1 = 5(2)5 = 160 The 6th term of the sequence is 160.

  15. Caution When writing a function rule for a sequence with a negative common ratio, remember to enclose r in parentheses. –212 ≠ (–2)12

  16. Lesson Quiz: Part I Find the next three terms in each geometric sequence. 1. 3, 15, 75, 375,… 2. 3. The first term of a geometric sequence is 300 and the common ratio is 0.6. What is the 7th term of the sequence? 4. What is the 15th term of the sequence 4, –8, 16, –32, 64…?

More Related