1 / 11

Chapter 12

Chapter 12. Sequences and Series. 12.3. Geometric Sequences and Series. Geometric Sequences and Series. a 1 a 2 a 3 a 4 a n. a 1 a 1 *r a 1 *r*r a 1 *r*r*r. a 1 a 1 *r a 1 *r 2 a 1 *r 3. a 1 *r n-1. Geometric Sequences have “r” the common ratio!

homert
Télécharger la présentation

Chapter 12

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. Chapter 12 Sequences and Series

  2. 12.3 Geometric Sequences and Series

  3. Geometric Sequences and Series • a1 • a2 • a3 • a4 • an • a1 • a1*r • a1*r*r • a1 *r*r*r • a1 • a1*r • a1*r2 • a1 *r3 • a1*rn-1 • Geometric Sequences have “r” the common ratio! • If the first term is 3 and the common ratio is 2 find the first four terms • 3, 6, 12, 24

  4. Finding the nth term of a Geometric Sequence: • an = a1rn-1 • a1 = first term • r = common ratio: a2 / a1 • n = term we are looking for

  5. Examples • Find the tenth term of 2, -10, 50 … • -3,906,250 • Find the tenth term of 1, 1/3, 1/9 … • 1/19,683 • Find the eight term of 5, 15, 45 … • 10,935

  6. Examples Cont. • If the third term of a geometric sequence is 63/4 and the sixth term is 1701/32 find the fifth term. • Hint a6 =a3*r3 • Therefore: 1701/32=63/4 r3 • And r = 3/2 • And the fifth term is 567/16

  7. Sum of a Geometric Series (Finite) • Find the sum of the first 10 terms: 1+0.7+0.49… • Approximately 3.2392… • Find the sum of the first 20 terms: 2 + -4 + 8 + -16 … • -699,050

  8. Examples Cont: • 7 + -14/3 + 28/9 … • 931/243

  9. Infinite Sum • Find the sum: 2 + 2/5 + 2/25 + … • 5/2 • Proof: write 0.33333… as a fraction • Write .454545… as a fraction • 5/11 • Write 2.351515151… as a fraction • 388/165

  10. What about?

  11. Homework • Pg 839-841: 1 – 5, 7 – 12, 24, 26, 30, 38 – 42 even, 45 - 47

More Related