1 / 7

Geometric Sequence

Geometric Sequence. Sequences and Series. Geometric Sequence. A sequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512,. geometric sequence. The common ratio , r , is 4. Find the common ratio of the following:. 1) 1, 2, 4, 8, 16, ... r = 2

herringtone
Download Presentation

Geometric Sequence

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. Geometric Sequence • Sequences and Series

  2. Geometric Sequence Asequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512, . . . geometric sequence The common ratio, r, is 4.

  3. Find the common ratio of the following: • 1) 1, 2, 4, 8, 16, ... • r = 2 • 2) 27, 9, 3, 1, 1/3, ... • r = 1/3 • 3) 3, 6, 12, 24, 48, ... • r = 2 • 4) 1/2, -1, 2, -4, 8, ... • r = -2

  4. Write the first 6 terms of the geometric sequence with the first term of 6 and common ratio of 1/3

  5. a2 = 15(5) a3 = 15(52) a4 = 15(53) The nth term of a geometric sequence has the form an = a1rn - 1 where r is the common ratio of consecutive terms of the sequence. a1 = 15 15, 75, 375, 1875, . . . The nth term is 15(5n-1).

  6. Example Find the 9th term of the geometric sequence 7, 21, 63, . . . a1 = 7 an = a1rn – 1 = 7(3)n – 1 a9 = 7(3)9 – 1 = 7(3)8 = 7(6561) = 45,927 6 The 9th term is 45,927.

  7. Your Turn Find the 8th term of the geometric sequence whose first term is -4 and whose common ratio is -2 a8 = -4(-128) = 512

More Related