Barisan dan Deret Geometri By Jeffrey Bivin Lake

Barisan dan Deret Geometri By: Jeffrey Bivin Lake Zurich High School jeff. bivin@lz 95. org. B Last Updated: October 11, 2005

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 , . . .

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

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

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

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

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

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

Menjumlahkan Deret Geometri Jeff Bivin -- LZHS

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

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

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

Tentukan jumlah barisan geometri Jeff Bivin -- LZHS

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

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

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

Deret Geometri Tak Hingga Jeff Bivin -- LZHS

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

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

Jumlah Deret Geometri Tak Hingga Jeff Bivin -- LZHS

Ingat --The Magic Flea Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

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

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

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

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

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

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

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

A Bouncing Ball L Turun = 625 + 375 + 225 + 135 + 81 + … = 1562. 5 L Naik = Jeff Bivin -- LZHS = 937. 5 TOTAL = 2500 ft. 375 + 225 + 135 + 81 + …

Menentukan jumlah tak hingga Jeff Bivin -- LZHS

Pecahan – Desimal Tak hingga Jeff Bivin -- LZHS

Mari kita coba kembali Jeff Bivin -- LZHS

Keunikan subtract Jeff Bivin -- LZHS

OK now a series Jeff Bivin -- LZHS

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