Barisan & deret bilangan
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Transcript of Barisan & deret bilangan
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Barisan & Deret Bilangan
Compiled by : Immanuelle Orchidea
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Barisan Aritmatika
• Barisan bilangan yang memiliki “beda” tetap
U1 U2 U3 U4
+b +b +b
Un = a (n-1) b ; a = U1
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Deret Aritmatika• Jumlah semua suku dari barisan aritmatika
Contoh :
Berapa jumlah semua bilangan asli dari
1- 100?
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1+ 2 + 3 + 4 +…………………+ 100 (a)
100+99+98+97+…………………+ 1 (b) +
101+ 101 +101+ 101 +…………...+ 101
Ada 100 bilangan 101 (100 x 101)Tapi kita hanya ingin tahu berapa jumlah deret (a)
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Jadi….
1+2+3+4+….+100 = (101) x 100
2
101 didapat dari 1 (suku pertama) ditambah 100 (suku terakhir)
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Barisan Geometri• Barisan bilangan
yang memiliki “perbandingan” tetap.
• Perbandingan = rasio = r
• U1 U2 U3 U4
• U2/U1 = U3/U2 = U4/U3 = r
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Konsep
U1 = a
U2 = a . r
U3 = a . r . r = ar2
U4 = a . r . r . r = ar3
……………………
Un = arn-1
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Deret Geometri• Jumlah semua suku dari
barisan geometri
• Berapakah jumlah total angka-angka dalam deret berikut ini?
2, 4, 8, …… U250
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• Sn = a + ar + ……+ arn-1
• kalikan dengan r• r x Sn = r x (a + ar + ……+ arn-1)
• Sn r = (ar + ar2 +…..+ arn )
..Hitung selisihnya..
Sn = a + ar + ar2 +……+ arn-1
Sn r = ar + ar2 +…..+ arn-1 + arn -
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Jadi..• Sn - Sn r = a – arn
• Sn (1-r) = a (1-rn)
Sn = a (1-rn)
(1-r)
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Fibonacci
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1, 1, 2, 3, 5, 8, 13, 21, 34…….
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Find it anywhere….
hurricane
Buildings
Ferns
flowers
Snail’s shells Spider web