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Arithmetic

Arithmetic. Sequences & Series By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: April 28, 2006. Arithmetic Sequences. 5, 8, 11, 14, 17, 20, … 3n+2, … -4, 1, 6, 11, 16, … 5n – 9, . . . 11, 7, 3, -1, -5, … -4n + 15,. Jeff Bivin -- LZHS.

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Arithmetic

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  1. Arithmetic Sequences & Series By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: April 28, 2006

  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, . . . Jeff Bivin -- LZHS

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

  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 Jeff Bivin -- LZHS

  5. Finding the nth term First term is -6 common difference is 7 an = a1 + d(n – 1) an = -6 + 7(n – 1) an = -6 + 7n – 7 an = 7n - 13 Jeff Bivin -- LZHS

  6. Finding the nth term First term is 23 common difference is -4 an = a1 + d(n – 1) an = 23 + -4(n – 1) an = 23 -4n +4 an = -4n + 27 Jeff Bivin -- LZHS

  7. Finding the 100th term a1 = 5 d = 6 n = 100 5, 11, 17, 23, 29, . . . an = a1 + d(n – 1) a100 = 5 + 6(100 – 1) a100 = 5 + 6(99) a100 = 5 + 594 a100 = 599 Jeff Bivin -- LZHS

  8. Finding 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 Jeff Bivin -- LZHS

  9. 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) Jeff Bivin -- LZHS

  10. Summing it up Sn = a1 + (a1 + d) + (a1 + 2d) + …+ an Sn = an + (an - d) + (an - 2d) + …+ a1 Jeff Bivin -- LZHS

  11. 1 + 4 + 7 + 10 + 13 + 16 + 19 a1 = 1 an = 19 n = 7 Jeff Bivin -- LZHS

  12. 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 a1 = 4 an = 24 n = 11 Jeff Bivin -- LZHS

  13. Find the sum of the integers from 1 to 100 a1 = 1 an = 100 n = 100 Jeff Bivin -- LZHS

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

  15. Find the sum of the multiples of 7 between 25 and 989 Sn = 28 + 35 + 42 + . . . + 987 a1 = 28 an = 987 d = 7 Jeff Bivin -- LZHS

  16. Evaluate Sn = 16 + 19 + 22 + . . . + 82 a1 = 16 an = 82 d = 3 n = 23 Jeff Bivin -- LZHS

  17. Evaluate Sn = -29 - 31 - 33 + . . . - 199 a1 = -29 an = -199 d = -2 n = 86 Jeff Bivin -- LZHS

  18. Find the sum of the multiples of 11 that are 4 digits in length Sn = 10 01+ 1012 + 1023 + ... + 9999 a1 = 1001 an = 9999 d = 11 Jeff Bivin -- LZHS

  19. Review -- Arithmetic Sum of n terms nth term Jeff Bivin -- LZHS

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