Question

Suku suku suatu barisan geometri memiliki nilai U1 +U2 =45 DAN U3 +U4 =20 rasio barisan geometri tersebut bernilai positif tentukan nilai u5 +u6

Answer 1

U1 + U2 = a + ar = 45
U3 + U4 = ar² + ar³ = 20
a + ar = 45
a (1 + r ) = 45
   (1 + r ) = 45 / a  .... (persamaan 1)
ar² + ar³ = 20
ar² (1 + r ) = 20 ..... substitusi persamaan 1
ar² . 45/a = 20
45 r² = 20
r² = 20/45
r² = 4/9
r = 2/3

a(1+ 2/3) = 45
a(5/3) = 45
a = 45 : 5/3
a = 45 × 3/5
   = 27

U5 + U6 = ar⁴ + ar⁵
               = 27.(2/3)⁴ + 27.(2/3)⁵
               = 27. 16/81 + 27. 32/243
               = 16/3 + 32/9
               = 48/9 + 32/9
               = 80/9