tentukan 2 suku berikutnya dan barisan bilangan berikut berdasarkan pola bilangan sebelumnya: a. 2,3,4,6,6,,12,8,...,... b. 3,7,11,18,...,... c. 1,2,5,14,...,..

Kelas : IX (3 SMP)
Materi : Barisan dan Deret
Kata Kunci : pola, bilangan

Pembahasan : 
Mari kita lihat soal tersebut.
Tentukan 2 suku berikutnya dari barisan bilangan berikut berdasarkan pola bilangan sebelumnya 
a. 2, 3, 4, 6, 6, 12, 8, ..., ... 
b. 3, 7, 11, 18, ..., ... 
c. 1, 2, 5, 14, ..., ... 
d. 81, 80, 27, 40, 9, ..., ... 
e. 1, 3, 4, 9, 9, 27, 16, ..., ...

Jawab :
a. 2, 3, 4, 6, 6, 12, 8, 24, 10

U₁ = 2 → U₃ = 4 (2 + 2)
U₃ = 4 → U₅ = 6 (4 + 2)
U₅ = 6 → U₇ = 8 (6 + 2)
U₇ = 8 → U₉ = 10 (8 + 2)

U₂ = 3 → U₄ = 6 (3 x 2)
U₄ = 6 → U₆ = 12 (6 x 2)
U₆ = 12 → U₈ =  24 (12 x 2)

b. 3, 7, 11, 18, 19, 29

U₁ = 3 → U₃ = 11 (3 + 8)
U₃ = 11 → U₅ = 19 (11 + 8)

U₂ = 7 → U₄ = 18 (7 + 11)
U₄ = 18 → U₆ = 29 (18 + 11)

c. 1, 2, 5, 14, 41, 122

U₁ = 1 → U₂ = 2 (1 + 1 = 1 + 3⁰)
U₂ = 2 → U₃ = 5 (2 + 3 = 2 + 3¹)
U₃ = 5 → U₄ = 14 (5 + 9 = 5 + 3²)
U₄ = 14 → U₅ = 41 (14 + 27 = 14 + 3³)
U₅ = 41 → U₆ = 122 (41 + 81 = 41 + 3⁴)

d. 81, 80, 27, 40, 9, 20, 3

U₁ = 81 → U₃ = 27 (81 : 3)
U₃ = 27 → U₅ = 9 (27 : 3)
U₅ = 9 → U₇ = 3 (9 : 3)

U₂ = 80 → U₄ = 40 (80 : 2)
U₄ = 40 → U₆ = 20 (40 : 2)

e. 1, 3, 4, 9, 9, 27, 16, 81, 25

U₁ = 1² = 1
U₃ = 2² = 4
U₅ = 3² = 9
U₇ = 4² = 16
U₉ = 5² = 25

U₂ = 3 → U₄ = 9 (3 x 3)
U₄ = 9 → U₆ = 27 (9 x 3)
U₆ = 27 → U₈ = 81 (27 x 3)


Semangat!