1 / 13

Ch 8.4

Ch 8.4. Finding Sums of Infinite Geometric Series. Warm Up Review: What is the difference between arithmetic and geometric sequences?. In a Arithmetic Sequence , the difference of consecutive terms is constant. This difference is called the common difference.

pleasants
Download Presentation

Ch 8.4

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. Ch 8.4 Finding Sums of Infinite Geometric Series

  2. Warm Up Review: What is the difference between arithmetic and geometric sequences? In a Arithmetic Sequence, the difference of consecutive terms is constant. This difference is called the common difference. In a Geometric Sequence, the ratio of any term to the previous term is constant. This constant ratio is called the common ratio. Talk with your groups about whether each sequence is arithmetic, geometric, or neither. C. d.

  3. How can we find the sum of an INFINTE geometric series? Given the following geometric series, determine the ratio and formula. a) 1 + r = ________ = _____________ b) 1 + r = ________ = _____________ c) 1 + r = ________ = _____________ d) 1 + r = ________ = _____________ e) 1 + r = ________ = _____________ Each of these series are infinite. Do you think we can find a sum for any of these?

  4. Grab a computer, open up to Google Sheets 1.99 1.99 Approx 2 Approx 1.5 1.49 1.5 Drastically diff sums 873 6648 Drastically diff sums 109 280255 7.94 ? 9.94

  5. EX 1: Find the sum of the infinite series. a) 1 + .1 + .01 + .001 + .0001 + …. B) 2 + + + … c) d) |r| = 0.6 which is less than 1 CANNOT find the sum because |r|>1 Sum =

  6. You Try! a) c) b) 3 + .3 + .03 + .003 + .0003 + …. D) 1 + 2 + 4 + 8 +16 + ….

  7. You Try! A child pushes a tumbler toy and lets it swing freely. On the first swing, the toy travels 30 centimeters. On each successive swing, the toy travels 75% of the distance of the previous swing. What is the total distance the toy swings?

  8. Classwork • pg 431 # 47, 49, 53, 54, 60 • Pg 439 # 3, 7-17odd

More Related