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# Barisan dan Deret Arit metika - PowerPoint PPT Presentation

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 Aritmetika

By: Jeffrey Bivin

Lake Zurich High School

jeff.bivin@lz95.org

Last Updated: April 28, 2006

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

Un = a + (n – 1)b

Un : suku ke n

a : suku pertama

b : beda

Jeff Bivin -- LZHS

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

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

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

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

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

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

Sn = a + (a+ b) + (a + 2b) + …+ Un

Sn = Un + (Un - b) + (Un - 2b) + …+ a

Jeff Bivin -- LZHS

a = 1

Un = 19

n = 7

Jeff Bivin -- LZHS

a = 4

Un = 24

n = 11

Jeff Bivin -- LZHS

Menentukan jumlah bilangan bulat dari 1 sampai 100

a = 1

Un = 100

n = 100

Jeff Bivin -- LZHS

Menentukan jumlah suku dengan beda 3 antara 9 dan 1344

Sn = 9 + 12 + 15 + . . . + 1344

a = 9

Un = 1344

b = 3

Jeff Bivin -- LZHS

MenentukanJumlahSuku dengan beda 7 antara 25 dan 989

Sn = 28 + 35 + 42 + . . . + 987

a = 28

Un = 987

b = 7

Jeff Bivin -- LZHS

Sn = 16 + 19 + 22 + . . . + 82

a1 = 16

an = 82

d = 3

n = 23

Jeff Bivin -- LZHS

Sn = -29 - 31 - 33 + . . . - 199

a = -29

Un = -199

b = -2

n = 86

Jeff Bivin -- LZHS

Menentukan Jumlah bilangan habis dibagi 11 dalan 4 digit

Sn = 10 01+ 1012 + 1023 + ... + 9999

a = 1001

Un = 9999

b = 11

Jeff Bivin -- LZHS

Rangkuman -- Aritmetika

Rumus Jumlah Suku ke n

Rumus Suku ke n

Jeff Bivin -- LZHS