Suku-suku barisan geometri tak hingga adalah positif . Jika jumlah suku u1 + u2 = 4t dan u3 + u4 = 20 , maka jumlah suku - suku barisan adalah

U1 + U2 = 45
a + ar = 45
a(1 + r) = 45
a = 45/(1 + r)

U3 + U4 = 20
ar² + ar³ = 20
ar²(1 + r) = 20

Substitusi...
45/(1 + r)r²(1 + r) = 20
45r² = 20
r² = 20/45
r = √[20/45]
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

[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\\9r^2=4\\r^2=\frac49\\r=\frac23\\\\a(1+r)=45\\a(1+\frac23)=45\\a(\frac53)=45\\a=27\\\\S_\infty=\frac{a}{1-r}\\S_\infty=\frac{27}{1-\frac23}\\S_\infty=\frac{27}{\frac13}\\\boxed{\boxed{S_\infty=81}}[/tex]