Question

Suatu barisan geometri diketahui bahwa U2+U3 = 24 dan U4+U6 = 5. Rasio deret geometri tersebut adalah....

Answer 1

U2 + u3 = 24
ar + ar² = 24
 ar(1+r) = 24 → a = 24/(r+r²)

   u4+u6 = 5
ar³ + ar⁵ = 5
ar³(1+r²) = 5

subtitusi a = 24/(r+r²)
        (24/(r+r²)).r³(1+r²) = 5
             24.(r²+r⁴)/(1+r) = 5
             24r⁴+24r²-5r-5 = 0
(2r-1)(12r³+6r²+15r+5) = 0

maka, r = 1/2