Question

Suku² geometri tak hingga adalah positif.jika jumlah suku U1+U2=45 dan U3+U4=20,maka jumlah suku² barisan itu adalah??

Answer 1

Verified answer

Answer 2

Verified answer

Mapel : Matematika
Kelas : XII SMA
Bab : Barisan dan Deret

Pembahasan :
U1 + U2 = 45
a + ar = 45
a(1 + r) = 45
a = 45/(1 + r) ——» Persamaan I

U3 + U4 = 20
ar² + ar³ = 20
ar²(1 + r) = 20 ——» Persamaan II

Substitusi...
ar²(1 + r) = 20
45/(1 + r) r²(1 + r) = 20
45r² = 20
r² = 20/45
r = √[20/45]
r = √[5.4/9.5]
r = √[4/9]
r = 2/3

a = 45/(1 + r)
a = 45/(1 + 2/3]
a = 45/(5/3)
a = 27

Maka...
S~ = a/(1 - r)
S~ = 27/(1 - 2/3)
S~ = 27/(1/3)
S~ = 81