1 / 26

Geometric

Geometric. Sequences & Series. Geometric Sequences. 1, 2, 4, 8, 16, 32, … 2 n-1 , … 3, 9, 27, 81, 243, … 3 n , . . . 81, 54, 36, 24, 16, … ,. n th term of geometric sequence. a n = a 1 ·r (n-1). Find the n th term of the geometric sequence. First term is 2

jaimie
Download Presentation

Geometric

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 Sequences & Series

  2. Geometric Sequences 1, 2, 4, 8, 16, 32, … 2n-1, … 3, 9, 27, 81, 243, … 3n, . . . 81, 54, 36, 24, 16, … , . . .

  3. nth term of geometric sequence an = a1·r(n-1)

  4. Find the nth term of thegeometric sequence First term is 2 Common ratio is 3 an = a1·r(n-1) an = 2(3)(n-1)

  5. EX1 Find the nth term of a geometric sequence a) First term is 128 Common ratio is (1/2) an = a1·r(n-1)

  6. Ex 1 Find the nth term of the geometric sequence b) First term is 64 Common ratio is (3/2) an = a1·r(n-1)

  7. c) Finding the 10th term a1 = 3 r = 2 n = 10 3, 6, 12, 24, 48, . . . an = a1·r(n-1) an = 3·(2)10-1 an = 3·(2)9 an = 3·(512) an = 1536

  8. d) Finding the 8th term a1 = 2 r = -5 n = 8 2, -10, 50, -250, 1250, . . . an = a1·r(n-1) an = 2·(-5)8-1 an = 2·(-5)7 an = 2·(-78125) an = -156250

  9. Sum it up

  10. 1 + 3 + 9 + 27 + 81 + 243 a1 = 1 r = 3 n = 6

  11. EX 2 Find the suma) 4 - 8 + 16 - 32 + 64 – 128 + 256 a1 = 4 r = -2 n = 7

  12. b) Evaluate = 2 + 4 + 8+…+1024 a1 = 2 r = 2 n = 10

  13. c) Evaluate = 3 + 6 + 12 +…+ 384 a1 = 3 r = 2 n = 8

  14. Review -- Geometric Sum of n terms nth term an = a1·r(n-1)

  15. Geometric Infinite Series

  16. Sum it up -- Infinity

  17. EX 3 Find the sum

  18. c) A Bouncing Ball rebounds ½ of the distance from which it fell -- What is the total vertical distance that the ball traveled before coming to rest if it fell from the top of a 128 feet tall building? 128 ft 64 ft 32 ft 16 ft 8 ft

  19. A Bouncing Ball Downward = 128 + 64 + 32 + 16 + 8 + … 128 ft 64 ft 32 ft 16 ft 8 ft

  20. A Bouncing Ball Upward = 64 + 32 + 16 + 8 + … 128 ft 64 ft 32 ft 16 ft 8 ft Jeff Bivin -- LZHS

  21. A Bouncing Ball Downward = 128 + 64 + 32 + 16 + 8 + … = 256 Upward = 64 + 32 + 16 + 8 + … = 128 TOTAL = 384 ft. 128 ft 64 ft 32 ft 16 ft 8 ft

  22. d) A Bouncing Ball rebounds 3/5 of the distance from which it fell -- What is the total vertical distance that the ball traveled before coming to rest if it fell from the top of a 625 feet tall building? 625 ft 375 ft 225 ft 135 ft 81 ft

  23. A Bouncing Ball Downward = 625 + 375 + 225 + 135 + 81 + … 625 ft 375 ft 225 ft 135 ft 81 ft

  24. A Bouncing Ball Upward = 375 + 225 + 135 + 81 + … 625 ft 375 ft 225 ft 135 ft 81 ft

  25. A Bouncing Ball Downward = 625 + 375 + 225 + 135 + 81 + … = 1562.5 Upward = 375 + 225 + 135 + 81 + … = 937.5 TOTAL = 2500 ft. 625 ft 375 ft 225 ft 135 ft 81 ft

More Related