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Barisan dan Deret Geometri By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.orgB Last Updated: October 11, 2005

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Barisan Geometri 1, 2, 4, 8, 16, 32, … 2 n-1, … 3, 9, 27, 81, 243, … 3 n,... 81, 54, 36, 24, 16, …,... Jeff Bivin -- LZHS

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Barisan Geometri Suku Ke-n U n = a·r (n-1) Jeff Bivin -- LZHS

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Menentukan Rumus Barisan Geometri Suku Pertama 2 Rasio 3 u n = a·r (n-1) u n = 2(3) (n-1) Jeff Bivin -- LZHS

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Tentukan rumus barisan geometri U n Suku Pertama 128 Rasio (1/2) U n = a·r (n-1) Jeff Bivin -- LZHS

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Tentukan rumus barisan geometri suku ke- n atau U n Suku pertama 64 Rasio (3/2) U n = a·r (n-1) Jeff Bivin -- LZHS

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Menentukan Nilai Suku Ke-10 3, 6, 12, 24, 48,... a = 3 r = 2 n = 10 U n = a·r (n-1) U 10 = 3·(2) 10-1 U 10 = 3·(2) 9 U 10 = 3·(512) U 10 = 1536 Jeff Bivin -- LZHS

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Menentukan Suku Ke-8 2, -10, 50, -250, 1250,... a= 2 r = -5 n = 8 U n = a·r (n-1) U n = 2·(-5) 8-1 U n = 2·(-5) 7 U n = 2·(-78125) U n = -156250 Jeff Bivin -- LZHS

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Menjumlahkan Deret Geometri Jeff Bivin -- LZHS

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1 + 3 + 9 + 27 + 81 + 243 a = 1 r = 3 n = 6 Jeff Bivin -- LZHS

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4 - 8 + 16 - 32 + 64 – 128 + 256 a = 4 r = -2 n = 7 Jeff Bivin -- LZHS

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Alternative Sum Formula Kita tahu bahwa: Dikalikan r: Sederhanakan: Substitusikan: Jeff Bivin -- LZHS

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Tentukan jumlah barisan geometri Jeff Bivin -- LZHS

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Hitunglah a = 2 r = 2 n = 10 U n = 1024 = 2 + 4 + 8+…+1024 Jeff Bivin -- LZHS

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Hitunglah a = 3 r = 2 n = 8 U n = 384 = 3 + 6 + 12 +…+ 384 Jeff Bivin -- LZHS

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Rangkuman -- Geometri Rumus Suku-n Jumlah Suku-n U n = a·r (n-1) Jeff Bivin -- LZHS

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Deret Geometri Tak Hingga Jeff Bivin -- LZHS

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The Magic Flea (magnified for easier viewing) There is no flea like a Magic Flea Jeff Bivin -- LZHS

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The Magic Flea (magnified for easier viewing) Jeff Bivin -- LZHS

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Jumlah Deret Geometri Tak Hingga Jeff Bivin -- LZHS

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Ingat --The Magic Flea Jeff Bivin -- LZHS

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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? Jeff Bivin -- LZHS

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A Bouncing Ball Lintasan Turun = 128 + 64 + 32 + 16 + 8 + … Jeff Bivin -- LZHS

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A Bouncing Ball Lintasan Naik= 64 + 32 + 16 + 8 + … Jeff Bivin -- LZHS

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A Bouncing Ball L Naik = 64 + 32 + 16 + 8 + … = 128 L Turun = 128 + 64 + 32 + 16 + 8 + … = 256 TOTAL = 384 ft. Jeff Bivin -- LZHS

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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? Jeff Bivin -- LZHS

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A Bouncing Ball L Turun= 625 + 375 + 225 + 135 + 81 + … Jeff Bivin -- LZHS

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A Bouncing Ball L Naik= 375 + 225 + 135 + 81 + … Jeff Bivin -- LZHS

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A Bouncing Ball L Naik = 375 + 225 + 135 + 81 + … = 937.5 L Turun = 625 + 375 + 225 + 135 + 81 + … = 1562.5 TOTAL = 2500 ft. Jeff Bivin -- LZHS

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Menentukan jumlah tak hingga Jeff Bivin -- LZHS

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Pecahan – Desimal Tak hingga Jeff Bivin -- LZHS

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Mari kita coba kembali Jeff Bivin -- LZHS

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Keunikan subtract Jeff Bivin -- LZHS

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OK now a series Jeff Bivin -- LZHS

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That’s All Folks.9 = 1 Jeff Bivin -- LZHS

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