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Barisan dan Deret Arit metika

Barisan dan Deret Arit metika. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: April 28, 2006. Barisan Aritmetika. 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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Barisan dan Deret Arit metika

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  1. Barisan dan Deret Aritmetika By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: April 28, 2006

  2. Barisan Aritmetika 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. Barisan Aritmetika Suku ke-n Un = a + (n – 1)b Un : suku ke n a : suku pertama b : beda Jeff Bivin -- LZHS

  4. Tentukan Rumus Barisan Aritmetika Un Suku pertama 8 Beda 3 Un = a + (n – 1)b Un = 8 + (n – 1)3 Un = 8 + 3n – 3 Un = 3n + 5 Jeff Bivin -- LZHS

  5. Menentukan Rumus Suku ke n Suku pertama -6 Beda 7 Un = a + (n – 1)b Un = -6 + (n – 1)7 Un = -6 + 7n – 7 Un = 7n - 13 Jeff Bivin -- LZHS

  6. Menentukan Rumus Un Suku pertama 23 Beda -4 Un = a + (n – 1)b Un = 23 + (n – 1)(-4) Un = 23 -4n +4 Un = -4n + 27 Jeff Bivin -- LZHS

  7. Menentukan Suku ke 100 a = 5 b = 6 n = 100 5, 11, 17, 23, 29, . . . Un = a + (n – 1)b U100 = 5 + (100 – 1)6 U100 = 5 + (99) 6 U100 = 5 + 594 U100 = 599 Jeff Bivin -- LZHS

  8. Menentukan Suku ke 956 a = 156 b = -16 n = 956 156, 140, 124, 108, . . . Un = a + (n – 1)b U956 = 156 +(956 – 1)(-16) U956 = 156 - (955) 16 U956 = 156 - 15280 U956 = -15124 Jeff Bivin -- LZHS

  9. Menentukan jumlah bilangan bulatdari 1 sampai 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. Rumus Jumlah Deret Aritmetika Sn = a + (a+ b) + (a + 2b) + …+ Un Sn = Un + (Un - b) + (Un - 2b) + …+ a Jeff Bivin -- LZHS

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

  12. 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24, Sn = ... a = 4 Un = 24 n = 11 Jeff Bivin -- LZHS

  13. Menentukan jumlah bilangan bulat dari 1 sampai 100 a = 1 Un = 100 n = 100 Jeff Bivin -- LZHS

  14. Menentukan jumlah suku dengan beda 3 antara 9 dan 1344 Sn = 9 + 12 + 15 + . . . + 1344 a = 9 Un = 1344 b = 3 Jeff Bivin -- LZHS

  15. MenentukanJumlahSuku dengan beda 7 antara 25 dan 989 Sn = 28 + 35 + 42 + . . . + 987 a = 28 Un = 987 b = 7 Jeff Bivin -- LZHS

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

  17. Hitung Sn = -29 - 31 - 33 + . . . - 199 a = -29 Un = -199 b = -2 n = 86 Jeff Bivin -- LZHS

  18. Menentukan Jumlah bilangan habis dibagi 11 dalan 4 digit Sn = 10 01+ 1012 + 1023 + ... + 9999 a = 1001 Un = 9999 b = 11 Jeff Bivin -- LZHS

  19. Rangkuman -- Aritmetika Rumus Jumlah Suku ke n Rumus Suku ke n Jeff Bivin -- LZHS

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