Pola Dan Barisan Bilangan(1)
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Transcript of Pola Dan Barisan Bilangan(1)
![Page 1: Pola Dan Barisan Bilangan(1)](https://reader035.fdocuments.mx/reader035/viewer/2022081415/55405b294a7959b41d8b4a68/html5/thumbnails/1.jpg)
POLA DAN BARISAN BILANGAN
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I. POLA BILANGAN
1. POLA BILANGAN GENAP
2. POLA BILANGAN GANJIL
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3. POLA BILANGAN PERSEGI PANJANG
4. POLA BILANGAN SEGITIGA
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5. POLA BILANGAN PERSEGI
6. POLA BILANGAN FIBONACI
a. 1 3 4 7 11 18 29,…
b. 1 1 2 3 5 8 13,…
c. - 2 3 1 4 5 9,...
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7. POLA BILANGAN SEGITIGA PASCAL 1
1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1
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II. BARISAN BILANGAN CONTOH : 1. 3 7 11 15 19 23 , … 2. 4 7 10 13 16 19 , … 3. 2 4 7 11 16 22 , … 4. 1/2 2/5 3/8 4/11 5/14 5. 20 13 7 2 - 2 - 5 - 7
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RUMUS SUKU KE- N ( Un ) CONTOH : 1. 5 7 9 11 13 suku ke 50….? Un = 2 n + 3 U50 = 2.50 + 3 = 100 + 3 = 103
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2. 2 9 16 23 30 37 U80 = ? Un = 7n - 5 U80 = 7.80 - 5 = 560 - 5 = 555
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3. - 2 1 4 7 10 13 U120 = ? Un = 3n - 5 U120 = 3. 120 - 5 = 360 - 5 = 355
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4. 30 21 12 3 - 6 -15 U 200 = ? Un = - 9n + 39 U200 = - 9 . 200 + 39 = - 1800 + 39 = -1761
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COBA KERJAKAN DEH !
1. 4 8 13 19 26,… 3 suku berikut ?2. 42 33 25 18 12 ,… 3 suku berikut ?3. 7 11 15 19 23 Un = ?4. 5 11 17 23 29 U180 = ?
5. 1 8 15 22 29 U300 = ?6. 42 34 26 18 10 U240 = ?
7. - 2 1 -1 0 -1 -1 -2 ,… 3 suku
berikut
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CONTOH SOAL 1. JIKA Un = 7n – 4 5 suku pertama ? U1 U2 U3 U4 U5 = ….
U1 = 7 . 1 – 4 U2 = 7 . 2 – 4 = 7 – 4 = 14 – 4 = 3 = 10 5 suku pertama : 3 10 17 24 31
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2. Un = - 8n + 27 5 suku pertama ? U1 = - 8.1 + 27 = - 8 + 27 = 19 19 11 3 -5 -13
U2 = - 8 . 2 + 27 = - 16 + 27 = 11
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3. Un = 7n – 1 4. Un = - 4n + 9 jika Un = 279 jika Un = - 171 tentukan n tentukan n
Un = 7n – 1 Un = - 4n + 9 279 = 7n – 1 - 171 = - 4n + 9 279 + 1 = 7n 4n = 9 + 171 280 = 7n 4n = 180 280 : 7 = n n = 180 : 4 40 = n n = 45
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L A T I H A N1. Un = 8n – 3 5 suku pertama …………?
2. Un = - 17n + 24 5 suku pertama……..?
3. Un = 9n – 4, jika Un = 176, tentukan n ?4. 4 11 18 25 32 , . . . jika Un = 557 , tentukan n ?5. Un = - 3n + 7 jika Un = - 203, tentukan n
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CONTOH SOAL1. JIKA Un = an + b dan U2 = 11,
U7 = 51, tentukan : a. rumus Un b. U47
Jawab
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a. Un = an + b, U2 = 11 2a + b = 11 U7 = 51 7a + b = 51 - 5a = - 40 a = -40 : - 5 a = 8 2a + b = 11 rumus Un = 8n – 5 2.8 + b = 11 16 + b = 11 b. U47 = …… ? b = 11 – 16 b = - 5
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2. Un = an + b
jika U3 = 9 , U5 = - 1 tentukan :
a. nilai a dan b
b. rumus Un
c. U60
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CONTOH SOAL1. Tulislah 10 bilangan asli yang pertama kemudian tentukan jumlah seluruhnya.2. Tulislah 10 bilangan kelipatan 7 yang pertama dan jumlahkan.3. Tulislah 100 bilangan ganjil yang pertama kemudian jumlahkan seluruhnya!!!!!!!
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RUMUS JUMLAH SUKU KE-N (Sn)
Sn = n( Un + U1)
2
1. jumlah 100 bilangan ganjil yang
pertama
1 3 5 7 9,… S100 = 100(199 + 1)
Un = 2n – 1 2
U100 = 2.100 – 1 = 50.200
= 199 = 10.000
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2. 3 7 11 15 19,… dit S80…?
Un = 4n – 1
U80 = 4.80 – 1
= 319
S80 = 80( 319 + 3 )
2
= 40. 322
= 12880
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3. 24 17 10 3 -4,… S120 = ?
Un = - 7n + 31
U120 = -7.120 + 31
= - 840 + 31
= - 809
S120 = 120( -809 + 24 )
2
= 60. – 785
= - 47100
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4. Dalam gedung bioskop, pada baris pertama
ada 15 kursi, tiap baris berikutnya
bertambah 3 kursi. Tentukan jumlah kursi
seluruhnya jika dalam bioskop itu ada
16 baris.