suku suku barisan geometri tak hingga adalah positif. Jika jumlah suku u1 + u2 = 45 dan u3 + u4 = 20, maka jumlah suku-suku barisan itu adalah...

Mapel : Matematika
Kelas : XI SMA
Bab : Barisan dan deret

Pembahasan :
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...
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

Substitusi...
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

Bab Barisan dan Deret
Matematika SMA Kelas XI

geometri tak hingga

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

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

1 + r = 1 + r
45/a = 20/(ar²)

coret a

r² = 20/45
r = √(4/9)
r = +- 2/3     → ambil yang positif
r = 2/3

1 + r = 45/a
a = 45 / (1 + r)

S∞ = a/(1 - r)
S∞ = (45/(1 + r)) . 1/(1 - r)
S∞ = 45 / (1 + 2/3) . 1/(1 - 2/3)
S∞ = 45 / (1 - 4/9)
S∞ = 45 . 9/5
S∞ = 81