1 / 12

6.3 Geometric Series

6.3 Geometric Series. 3/25/2013. Geometric Sequence:. Is a sequence where each term is multiplied by the same factor in order to obtain the following term . Example:. 2, 8, 32, 128, 512, . . . . x 4 . x 4 . x 4 . x 4 . Common ratio (r):. 4 . Definition of Geometric Sequence.

perrin
Download Presentation

6.3 Geometric Series

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. 6.3 Geometric Series 3/25/2013

  2. Geometric Sequence: Is a sequence where each term is multiplied by the same factor in order to obtain the following term. Example: 2, 8, 32, 128, 512, . . . x 4 x 4 x 4 x 4 Common ratio (r): 4

  3. Definition of Geometric Sequence Rule of nth term of a geometric sequence 2, 8, 32, 128, 512, . . . Common ratio, r = 4 1st term: 2nd term: 3rd term: 4th term: What’s the pattern? Rule:

  4. Geometric Series: Expression formed by adding the terms of a geometric sequence. Example (Finite): r Geometric Infinite Series: r

  5. Determine whether the following series is geometric. Explain why or why not. If it is geometric, find the common ratio. Yes Each term is multiplied by 5. r = 5 • Yes • Each term is multiplied by . • r = . No Each term is multiplied by different values. No Each term is multiplied by different values.

  6. Sum of the Finite Geometric Series S = Sum of the series = first term in the series. r = common ratio n = number of terms.

  7. Find the sum of the finite geometric series ++ r = 4 n = since n started at 0 there are 9 terms = 524,286

  8. Find the sum of the finite geometric series r = n = 15 = 13.999957

  9. Sum of the Infinite Geometric Series Only when common ratio is between 0 and 1. S = Sum of the series = first term in the series. r = common ratio

  10. Find the sum of the infinite geometric series r = = 14

  11. Find the sum of the infinite geometric series r = =

  12. Homework WS 6.3 odd problems only “I stayed up all night to see where the sun went. Then it dawned on me.”

More Related