1 / 17

Notes 9.2

Notes 9.2. Arithmetic Sequence & Series. Arithmetic Sequences. 5, 8, 11, 14, 17, 20, … 3n+2, … -4, 1, 6, 11, 16, … 5n – 9, . . . 11, 7, 3, -1, -5, … -4n + 15,. An Arithmetic sequence has a common difference. n th term of arithmetic sequence. a n = a 1 + d(n – 1).

satya
Download Presentation

Notes 9.2

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. Notes 9.2 Arithmetic Sequence & Series

  2. Arithmetic Sequences 5, 8, 11, 14, 17, 20, … 3n+2, … -4, 1, 6, 11, 16, … 5n – 9, . . . 11, 7, 3, -1, -5, … -4n + 15, . . . An Arithmetic sequence has a common difference

  3. nth term of arithmetic sequence an = a1 + d(n – 1)

  4. Find the nth term of an arithmetic sequence First term is 8 Common difference is 3 an = a1 + d(n – 1) an = 8 + 3(n – 1) an = 8 + 3n – 3 an = 3n + 5

  5. Example 1: find the formula for the nth term a) First term is -6 difference is 7 an = a1 + d(n – 1) an = -6 + 7(n – 1) an = -6 + 7n – 7 an = 7n - 13 b) First term is 23 difference is -4 an = a1 + d(n – 1) an = 23 + -4(n – 1) an = 23 -4n +4 an = -4n + 27

  6. Example 2: Find the indicated term.a) 100th term 5, 11, 17, 23, 29, . . . an = a1 + d(n – 1) a100 = 5 + 6(100 – 1) a100 = 5 + 6(99) a100 = 5 + 594 a100 = 599 a1 = 5 d = 6 n = 100

  7. b) the 956th term a1 = 156 d = -16 n = 956 156, 140, 124, 108, . . . an = a1 + d(n – 1) a956 = 156 + -16(956 – 1) a956 = 156 - 16(955) a956 = 156 - 15280 a956 = -15124

  8. Find the Sum of the integers from 1 to 100 S100 = 1 + 2 + 3 +…+ 49 + 50 + 51 + 52 +…+ 98 + 99 + 100 S100 = 100 + 99 + 98 +…+ 52+51 + 50 + 49 +…+ 3 + 2 + 1 2S100 = 101+101+101+…+101+101+101+101+…+101+101+101 2S100 = 100 (101)

  9. Summing it up Sn = a1 + (a1 + d) + (a1 + 2d) + …+ an Sn = an + (an - d) + (an - 2d) + …+ a1

  10. Find the sum of the integers from 1 to 100 a1 = 1 an = 100 n = 100

  11. Example 3: Find the suma) 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 a1 = 4 an = 24 n = 11

  12. EX3 b)1 + 4 + 7 + 10 + 13 + 16 + 19 a1 = 1 an = 19 n = 7

  13. Find the sum of the multiples of 3 between 9 and 1344 a1 = 9 an = 1344 d = 3 Sn = 9 + 12 + 15 + . . . + 1344 Jeff Bivin -- LZHS

  14. Ex 3 c) Find the sum of the multiples of 7 between 25 and 989 a1 = 28 an = 987 d = 7 Sn = 28 + 35 + 42 + . . . + 987

  15. Evaluate a1 = 16 an = 82 d = 3 n = 23 Sn = 16 + 19 + 22 + . . . + 82

  16. Ex3 d) Evaluate a1 = -29 an = -199 d = -2 n = 86 Sn = -29 - 31 - 33 + . . . - 199

  17. Review -- Arithmetic Sum of n terms nth term

More Related