misalkan Un adalah suku ke-n dari sebuah barisan geometri. jika u2+u3=5 dan u4=4/3, maka u1 = ....

materi: barisan dan deret
kata kunci: barisan geometri

pembahasan di gambar

Matematika IX SMP
→→ Barisan dan deret ←←

Pembahasan :
U2 + U3 = 5
ar + ar² = 5
ar(1 + r) = 5
ar = 5/(1 + r)

U4 = 4/3
ar³ = 4/3
ar = 4/(3r²)

Samakan...
ar = ar
5/(1 + r) = 4/(3r²)
15r² = 4 + 4r
15r² - 4r - 4 = 0
(5r + 2)(3r - 2) = 0
r = -2/5
t = 2/3

Jika r = -2/5, maka...
ar³ = 4/3
a(-2/5)³ = 4/3
a(-8/125) = 4/3
a = (4/3)/(-8/125)
a = - 500/24
a = -250/12
a = -125/6

Jika r = 2/3, maka...
ar³ = 4/3
a(2/3)³ = 4/3
a(8/27) = 4/3
a = (4/3)/(8/27)
a = 108/24
a = 54/12
a = 27/6
a = 9/2