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Barisan dan Deret Geometri By: Jeffrey Bivin Lake Zurich High School Last Updated: October 11, 2005.

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Presentation on theme: "Barisan dan Deret Geometri By: Jeffrey Bivin Lake Zurich High School Last Updated: October 11, 2005."— Presentation transcript:

1 Barisan dan Deret Geometri By: Jeffrey Bivin Lake Zurich High School Last Updated: October 11, 2005

2 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

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

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

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

6 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

7 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

8 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 = Jeff Bivin -- LZHS

9 Menjumlahkan Deret Geometri Jeff Bivin -- LZHS

10 a = 1 r = 3 n = 6 Jeff Bivin -- LZHS

11 – a = 4 r = -2 n = 7 Jeff Bivin -- LZHS

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

13 Tentukan jumlah barisan geometri Jeff Bivin -- LZHS

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

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

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

17 Deret Geometri Tak Hingga Jeff Bivin -- LZHS

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

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

20 Jumlah Deret Geometri Tak Hingga Jeff Bivin -- LZHS

21 Ingat --The Magic Flea Jeff Bivin -- LZHS

22

23 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

24 A Bouncing Ball Lintasan Turun = … Jeff Bivin -- LZHS

25 A Bouncing Ball Lintasan Naik= … Jeff Bivin -- LZHS

26 A Bouncing Ball L Naik = … = 128 L Turun = … = 256 TOTAL = 384 ft. Jeff Bivin -- LZHS

27 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

28 A Bouncing Ball L Turun= … Jeff Bivin -- LZHS

29 A Bouncing Ball L Naik= … Jeff Bivin -- LZHS

30 A Bouncing Ball L Naik = … = L Turun = … = TOTAL = 2500 ft. Jeff Bivin -- LZHS

31 Menentukan jumlah tak hingga Jeff Bivin -- LZHS

32 Pecahan – Desimal Tak hingga Jeff Bivin -- LZHS

33 Mari kita coba kembali Jeff Bivin -- LZHS

34 Keunikan subtract Jeff Bivin -- LZHS

35 OK now a series Jeff Bivin -- LZHS

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


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