Dari barisan geometri, diketahui U2 = 27 dan U4 = 3. Jumlah 8 suku pertama barisan tersebut adalah..

Diketahui:

U2 = a . r = 27

U4 = a . r^3 = 3

Ditanyakan:

S8 = … ?

Penyelesaian:

cari rasio deret

r^3/r = 3/27

r^2 = 1/9

r = 1/3

suku pertama

a . r^3 = 3

a . (1/3)^3 = 3

a . 1/27 = 3

a = 81

Sn = a (1 – r^n)/(1 – r)

S8 = 81 (1 – (1/3)^8))/(1 – 1/3)

S8 = 81 (6.560/6.561)/(2/3)

S8 = 243/2 . 6560/6561

S8 = 3.280/27

S8 = 121 13/27

==================

Detil Jawaban

Kelas: 9

Mapel: Matematika

Bab: Barisan dan Deret Bilangan

Kode: 9.2.2

Kata Kunci: Deret Geometri

Penjelasan dengan langkah-langkah:

r = ^(4 – 2)√(U4 : U2)

r = ²√(3 : 27)

r = √(1/9)

r = 1/3

a = U2 : r

a = 27 : 1/3

a = 27 . 3/1

a = 81

Sn = a . (1 – r^n)/(1 – r)

S8 = 81 . (1 – (1/3)^8)/(3/3 – 1/3)

S8 = 81 . (6.561/6.561 – 1/6.561) / (2/3)

S8 = 81 . 6.560/6.561 . 3/2

S8 = 3.280/27

S8 = 121 14/27

Kelas 9

Pelajaran Matematika

Bab Barisan dan Deret Bilangan