1.1 Barisan Fibonacci

Tugas Kelompok Fibonacci

Ika Komalasari 1384202072May Rizki Herawati 1384202041

Okky Athfinati 1284202118Wulan Rahmawati 1384202094

March 10, 2016

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Barisan Fibonacci

1 1.1 Barisan Fibonacci

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Definisi

Barisan f0, f1, f2, f3, ..., fn − 2, fn − 1, fn disebut Fibonacci jika untukf0 = 1, f1 = 0 + f0, f2 = f0 + f1,f3 = f2 + f1,...,fn = fn − 2 + fn − 1

contoh barisan fibonacci1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Definisi

Barisan f0, f1, f2, f3, ..., fn − 2, fn − 1, fn disebut Fibonacci jika untukf0 = 1, f1 = 0 + f0, f2 = f0 + f1,f3 = f2 + f1,...,fn = fn − 2 + fn − 1

contoh barisan fibonacci1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Algoritma nilai optimal dengan Metode Fibonacci

Dicari nilai n terkecil

1

Fn+1<

2δ

L

dibentukL0 = Fn+1Ln

dibentuk

λi = ai +F(n+1)−i−1

F(n+1)−i+1(bi − ai )

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Algoritma nilai optimal dengan Metode Fibonacci

Dicari nilai n terkecil

1

Fn+1<

2δ

L

dibentukL0 = Fn+1Ln

dibentuk

λi = ai +F(n+1)−i−1

F(n+1)−i+1(bi − ai )

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Algoritma nilai optimal dengan Metode Fibonacci

Dicari nilai n terkecil

1

Fn+1<

2δ

L

dibentukL0 = Fn+1Ln

dibentuk

λi = ai +F(n+1)−i−1

F(n+1)−i+1(bi − ai )

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µi = ai +F(n+1)−i

F(n+1)−i+1(bi − ai )

jikaf (µi ) > f (λi )

ambil µi dan ai , masing-masing sebagai bi+1 dan ai+1

iterasi berhenti ketika bi − ai < 2δ

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µi = ai +F(n+1)−i

F(n+1)−i+1(bi − ai )

jikaf (µi ) > f (λi )

ambil µi dan ai , masing-masing sebagai bi+1 dan ai+1

iterasi berhenti ketika bi − ai < 2δ

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µi = ai +F(n+1)−i

F(n+1)−i+1(bi − ai )

jikaf (µi ) > f (λi )

ambil µi dan ai , masing-masing sebagai bi+1 dan ai+1

iterasi berhenti ketika bi − ai < 2δ

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Soal

minimalkanf (x) = 2x2 − 16x

dengan δ = 0, 1 pada selang 1 <= x <= 6

dengan cara analitik, diperoleh nilai x yang meminimalkanf (x) adalah x = 4

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Soal

minimalkanf (x) = 2x2 − 16x

dengan δ = 0, 1 pada selang 1 <= x <= 6

dengan cara analitik, diperoleh nilai x yang meminimalkanf (x) adalah x = 4

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Dengan cara metode numerik Fibonacci

Cari nilai n terkecil

1

Fn+1<

2δ

L

1

F8<

0, 2

5

1

34<

1

25

Jadi n terkecil = 7

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

Dengan cara metode numerik Fibonacci

Cari nilai n terkecil

1

Fn+1<

2δ

L

1

F8<

0, 2

5

1

34<

1

25

Jadi n terkecil = 7

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ1 = a1 +F(n+1)−1−1

F(n+1)−1+1(b1 − a1)

λ1 = 1 +F(8)−1−1

F(8)−1+1(6 − 1)

λ1 = 1 +F(6)F(8)

(5)

λ1 = 1 +(13)

(34)(5)

λ1 = 1 + 1, 912

λ1 = 2, 912

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ1 = a1 +F(n+1)−1−1

F(n+1)−1+1(b1 − a1)

λ1 = 1 +F(8)−1−1

F(8)−1+1(6 − 1)

λ1 = 1 +F(6)F(8)

(5)

λ1 = 1 +(13)

(34)(5)

λ1 = 1 + 1, 912

λ1 = 2, 912

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ1 = a1 +F(n+1)−1−1

F(n+1)−1+1(b1 − a1)

λ1 = 1 +F(8)−1−1

F(8)−1+1(6 − 1)

λ1 = 1 +F(6)F(8)

(5)

λ1 = 1 +(13)

(34)(5)

λ1 = 1 + 1, 912

λ1 = 2, 912

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ1 = a1 +F(n+1)−1−1

F(n+1)−1+1(b1 − a1)

λ1 = 1 +F(8)−1−1

F(8)−1+1(6 − 1)

λ1 = 1 +F(6)F(8)

(5)

λ1 = 1 +(13)

(34)(5)

λ1 = 1 + 1, 912

λ1 = 2, 912

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ1 = a1 +F(n+1)−1−1

F(n+1)−1+1(b1 − a1)

λ1 = 1 +F(8)−1−1

F(8)−1+1(6 − 1)

λ1 = 1 +F(6)F(8)

(5)

λ1 = 1 +(13)

(34)(5)

λ1 = 1 + 1, 912

λ1 = 2, 912

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ1 = a1 +F(n+1)−i

F(n+1)−1+1(b1 − a1)

µ1 = 1 +F(8)−1

F(8)−1+1(6 − 1)

µ1 = 1 +F(7)F(8)

(5)

µ1 = 1 +(21)

(34)(5)

µ1 = 1 + 3, 088

µ1 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ1 = a1 +F(n+1)−i

F(n+1)−1+1(b1 − a1)

µ1 = 1 +F(8)−1

F(8)−1+1(6 − 1)

µ1 = 1 +F(7)F(8)

(5)

µ1 = 1 +(21)

(34)(5)

µ1 = 1 + 3, 088

µ1 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ1 = a1 +F(n+1)−i

F(n+1)−1+1(b1 − a1)

µ1 = 1 +F(8)−1

F(8)−1+1(6 − 1)

µ1 = 1 +F(7)F(8)

(5)

µ1 = 1 +(21)

(34)(5)

µ1 = 1 + 3, 088

µ1 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ1 = a1 +F(n+1)−i

F(n+1)−1+1(b1 − a1)

µ1 = 1 +F(8)−1

F(8)−1+1(6 − 1)

µ1 = 1 +F(7)F(8)

(5)

µ1 = 1 +(21)

(34)(5)

µ1 = 1 + 3, 088

µ1 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ1 = a1 +F(n+1)−i

F(n+1)−1+1(b1 − a1)

µ1 = 1 +F(8)−1

F(8)−1+1(6 − 1)

µ1 = 1 +F(7)F(8)

(5)

µ1 = 1 +(21)

(34)(5)

µ1 = 1 + 3, 088

µ1 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ1 = a1 +F(n+1)−i

F(n+1)−1+1(b1 − a1)

µ1 = 1 +F(8)−1

F(8)−1+1(6 − 1)

µ1 = 1 +F(7)F(8)

(5)

µ1 = 1 +(21)

(34)(5)

µ1 = 1 + 3, 088

µ1 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicariF (λ1) = 2λ1

2 − 16λ1

= 2(2, 912)2 − 16(2, 912)

= 16, 959 − 46, 592

= −29, 633

dicariF (µ1) = 2µ1

2 − 16µ1

= 2(4, 088)2 − 16(4, 088)

= 33, 423 − 65, 408

= −31, 985

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

f (λ1) > f (µ1)

ambil λ1 dan b1 sebagai:

λ1 = a2

b1 = b2

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ2 = a2 +F(n+1)−i−1

F(n+1)−i+1(b2 − a2)

λ2 = 2, 912 +F(8)−2−1

F(8)−2+1(6 − 2, 912)

λ2 = 2, 912 +F(5)F(7)

(3.088)

λ2 = 2, 912 +(8)

(21)(3, 088)

λ2 = 2, 912 + 1, 176

λ2 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ2 = a2 +F(n+1)−i−1

F(n+1)−i+1(b2 − a2)

λ2 = 2, 912 +F(8)−2−1

F(8)−2+1(6 − 2, 912)

λ2 = 2, 912 +F(5)F(7)

(3.088)

λ2 = 2, 912 +(8)

(21)(3, 088)

λ2 = 2, 912 + 1, 176

λ2 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ2 = a2 +F(n+1)−i−1

F(n+1)−i+1(b2 − a2)

λ2 = 2, 912 +F(8)−2−1

F(8)−2+1(6 − 2, 912)

λ2 = 2, 912 +F(5)F(7)

(3.088)

λ2 = 2, 912 +(8)

(21)(3, 088)

λ2 = 2, 912 + 1, 176

λ2 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ2 = a2 +F(n+1)−i−1

F(n+1)−i+1(b2 − a2)

λ2 = 2, 912 +F(8)−2−1

F(8)−2+1(6 − 2, 912)

λ2 = 2, 912 +F(5)F(7)

(3.088)

λ2 = 2, 912 +(8)

(21)(3, 088)

λ2 = 2, 912 + 1, 176

λ2 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ2 = a2 +F(n+1)−i−1

F(n+1)−i+1(b2 − a2)

λ2 = 2, 912 +F(8)−2−1

F(8)−2+1(6 − 2, 912)

λ2 = 2, 912 +F(5)F(7)

(3.088)

λ2 = 2, 912 +(8)

(21)(3, 088)

λ2 = 2, 912 + 1, 176

λ2 = 4, 088

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ2 = a2 +F(n+1)−i

F(n+1)−i+1(b2 − a2)

µ2 = 2, 912 +F(8)−2

F(8)−2+1(6 − 2, 912)

µ2 = 2, 912 +F(6)F(7)

(3, 088)

µ2 = 2, 912 +(13)

(21)(3, 088)

µ2 = 2, 912 + 1, 912

µ2 = 4, 824

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ2 = a2 +F(n+1)−i

F(n+1)−i+1(b2 − a2)

µ2 = 2, 912 +F(8)−2

F(8)−2+1(6 − 2, 912)

µ2 = 2, 912 +F(6)F(7)

(3, 088)

µ2 = 2, 912 +(13)

(21)(3, 088)

µ2 = 2, 912 + 1, 912

µ2 = 4, 824

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ2 = a2 +F(n+1)−i

F(n+1)−i+1(b2 − a2)

µ2 = 2, 912 +F(8)−2

F(8)−2+1(6 − 2, 912)

µ2 = 2, 912 +F(6)F(7)

(3, 088)

µ2 = 2, 912 +(13)

(21)(3, 088)

µ2 = 2, 912 + 1, 912

µ2 = 4, 824

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ2 = a2 +F(n+1)−i

F(n+1)−i+1(b2 − a2)

µ2 = 2, 912 +F(8)−2

F(8)−2+1(6 − 2, 912)

µ2 = 2, 912 +F(6)F(7)

(3, 088)

µ2 = 2, 912 +(13)

(21)(3, 088)

µ2 = 2, 912 + 1, 912

µ2 = 4, 824

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ2 = a2 +F(n+1)−i

F(n+1)−i+1(b2 − a2)

µ2 = 2, 912 +F(8)−2

F(8)−2+1(6 − 2, 912)

µ2 = 2, 912 +F(6)F(7)

(3, 088)

µ2 = 2, 912 +(13)

(21)(3, 088)

µ2 = 2, 912 + 1, 912

µ2 = 4, 824

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ2 = a2 +F(n+1)−i

F(n+1)−i+1(b2 − a2)

µ2 = 2, 912 +F(8)−2

F(8)−2+1(6 − 2, 912)

µ2 = 2, 912 +F(6)F(7)

(3, 088)

µ2 = 2, 912 +(13)

(21)(3, 088)

µ2 = 2, 912 + 1, 912

µ2 = 4, 824

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicariF (λ2) = 2λ2

2 − 16λ2

= 2(4, 088)2 − 16(4, 088)

= 33, 423 − 65, 408

= −31, 985

dicariF (µ2) = 2µ2

2 − 16µ2

= 2(4, 824)2 − 16(4, 824)

= 46, 542 − 77, 184

= −30, 642

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

f (λ2) < f (µ2)

ambil µ2 dan a2 sebagai:

µ2 = b3

a2 = a3

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ3 = a3 +F(n+1)−i−1

F(n+1)−i+1(b3 − a3)

λ3 = 2, 912 +F(8)−3−1

F(8)−3+1(4, 824 − 2, 912)

λ3 = 2, 912 +F(4)F(6)

(1, 912)

λ3 = 2, 912 +(5)

(13)(1, 912)

λ3 = 2, 912 + 0, 735

λ3 = 3, 647

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ3 = a3 +F(n+1)−i−1

F(n+1)−i+1(b3 − a3)

λ3 = 2, 912 +F(8)−3−1

F(8)−3+1(4, 824 − 2, 912)

λ3 = 2, 912 +F(4)F(6)

(1, 912)

λ3 = 2, 912 +(5)

(13)(1, 912)

λ3 = 2, 912 + 0, 735

λ3 = 3, 647

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ3 = a3 +F(n+1)−i−1

F(n+1)−i+1(b3 − a3)

λ3 = 2, 912 +F(8)−3−1

F(8)−3+1(4, 824 − 2, 912)

λ3 = 2, 912 +F(4)F(6)

(1, 912)

λ3 = 2, 912 +(5)

(13)(1, 912)

λ3 = 2, 912 + 0, 735

λ3 = 3, 647

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ3 = a3 +F(n+1)−i−1

F(n+1)−i+1(b3 − a3)

λ3 = 2, 912 +F(8)−3−1

F(8)−3+1(4, 824 − 2, 912)

λ3 = 2, 912 +F(4)F(6)

(1, 912)

λ3 = 2, 912 +(5)

(13)(1, 912)

λ3 = 2, 912 + 0, 735

λ3 = 3, 647

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

λ3 = a3 +F(n+1)−i−1

F(n+1)−i+1(b3 − a3)

λ3 = 2, 912 +F(8)−3−1

F(8)−3+1(4, 824 − 2, 912)

λ3 = 2, 912 +F(4)F(6)

(1, 912)

λ3 = 2, 912 +(5)

(13)(1, 912)

λ3 = 2, 912 + 0, 735

λ3 = 3, 647

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ3 = a3 +F(n+1)−i

F(n+1)−i+1(b3 − a3)

µ3 = 2, 912 +F(8)−3

F(8)−3+1(4, 824 − 2, 912)

µ3 = 2, 912 +F(5)F(6)

(1, 912)

µ3 = 2, 912 +(8)

(13)(1, 912)

µ3 = 2, 912 + 1, 177

µ2 = 4, 089

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ3 = a3 +F(n+1)−i

F(n+1)−i+1(b3 − a3)

µ3 = 2, 912 +F(8)−3

F(8)−3+1(4, 824 − 2, 912)

µ3 = 2, 912 +F(5)F(6)

(1, 912)

µ3 = 2, 912 +(8)

(13)(1, 912)

µ3 = 2, 912 + 1, 177

µ2 = 4, 089

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ3 = a3 +F(n+1)−i

F(n+1)−i+1(b3 − a3)

µ3 = 2, 912 +F(8)−3

F(8)−3+1(4, 824 − 2, 912)

µ3 = 2, 912 +F(5)F(6)

(1, 912)

µ3 = 2, 912 +(8)

(13)(1, 912)

µ3 = 2, 912 + 1, 177

µ2 = 4, 089

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ3 = a3 +F(n+1)−i

F(n+1)−i+1(b3 − a3)

µ3 = 2, 912 +F(8)−3

F(8)−3+1(4, 824 − 2, 912)

µ3 = 2, 912 +F(5)F(6)

(1, 912)

µ3 = 2, 912 +(8)

(13)(1, 912)

µ3 = 2, 912 + 1, 177

µ2 = 4, 089

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ3 = a3 +F(n+1)−i

F(n+1)−i+1(b3 − a3)

µ3 = 2, 912 +F(8)−3

F(8)−3+1(4, 824 − 2, 912)

µ3 = 2, 912 +F(5)F(6)

(1, 912)

µ3 = 2, 912 +(8)

(13)(1, 912)

µ3 = 2, 912 + 1, 177

µ2 = 4, 089

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicari

µ3 = a3 +F(n+1)−i

F(n+1)−i+1(b3 − a3)

µ3 = 2, 912 +F(8)−3

F(8)−3+1(4, 824 − 2, 912)

µ3 = 2, 912 +F(5)F(6)

(1, 912)

µ3 = 2, 912 +(8)

(13)(1, 912)

µ3 = 2, 912 + 1, 177

µ2 = 4, 089

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

dicariF (λ3) = Fλ23 − 16λ3

= 2(3, 647)2 − 16(3, 647)

= 26, 601 − 58, 352

= −31, 751

dicariF (µ3) = 2µ23 − 16µ

= 2(4, 089)2 − 16(4, 089)

= 33, 439 − 65, 424

= −31, 985

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

lanjutan

f (λ3) > f (µ3)

ambil λ3 dan b3 sebagai:

λ3 = a4

b3 = b4

Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci

1.1 Barisan Fibonacci

x∗ = ai +(bi − ai )

2

= 3, 794 +(3, 942 − 3, 794)

2= 3, 794 + 0, 074

= 3, 868Ika Komalasari 1384202072May Rizki Herawati 1384202041Okky Athfinati 1284202118Wulan Rahmawati 1384202094Tugas Kelompok Fibonacci