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

[tex]\displaystyle u_1+u_2=45\\a+ar=45\\a(1+r)=45\\1+r=\frac{45}{a}\\\\u_3+u_4=20\\ar^2+ar^3=20\\ar^2(1+r)=20\\ar^2\cdot\frac{45}{a}=20\\45r^2=20\\r^2=\frac49\\r=\frac23\\\\1+r=\frac{45}{a}\\1+\frac23=\frac{45}{a}\\\frac53=\frac{45}{a}\\a=27\\\\S=\frac{a}{1-r}\\S=\frac{27}{1-\frac23}\\S=\frac{27}{\frac13}\\\boxed{\boxed{S=81}}[/tex]

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