Jawaban:

C. 6

Penjelasan dengan langkah-langkah:

tiga buah bilangan geometri

U₁ , U₂ , U₃

jumlah ke tiga bilangan = 19

U₁ + U₂ + U₃ = 19

a + ar + ar² = 19

ar² = 19 - (a + ar) ............, (1)

selisih bilangan terbesar dan terkecil = 5

U₃ - U₁ = 5

ar² - a = 5

ar² = a + 5 ....................... (2)

persamaan (2) = (1)

a + 5 = 19 - (a + ar)

a + (a + ar) = 19 - 5

2a + ar = 14

a(2 + r) = 14

a = 14/(2 + r) .................... (3)

subtitusikan (3) ke (1)

ar² = a + 5

[14/(2 + r)] x r² = [14/(2 + r)] + 5

[14r²/(2 + r)] = [14/(2 + r) + 5(2 + r)/(2 + r)]

[14r²/(2 + r)] = [(14 + 10 + 5r)/(2 + r)]

[14r²/(2 + r)] = [(24 + 5r)/2 + r)]

14r² = 24 + 5r

14r² - 5r - 24 = 0

(7r + 8)(2r - 3) = 0

7r + 8 = 0

7r = -8

r = -8/7 (tidak memenuhi karena negatif)

2r - 3 = 0

2r = 3

r = 3/2 ............................. (4)

subtitusikan ke (3)

a = 14/(2 + r)

a = 14/(2 + 3/2)

a = 14/(7/2)

a = 14 x 2/7

a = 4

suku ke dua (U₂)

U₂ = ar

U₂ = 4 x 3/2

U₂ = 6

barisan bilangannya

4 , 6, 9, ..........