Answer: B) 2/9
Step-by-step explanation:
Sum = a / (1 - r)
3 = a / (1 - r) ----(1)
Sum of cubes = a^3 / (1 - r^3)
27/19 = a^3 / (1 - r^3) ----(2)
a = 3(1 - r)
27/19 = (3(1 - r))^3 / (1 - r^3)
27/19 = (27(1 - r)^3) / (1 - r^3)
27/19 = (1 - r)^3 / (1 - r^3)
27(1 - r^3) = 19(1 - r)^3
27 - 27r^3 = 19 - 57r + 57r^2 - 57r^3
30r^3 + 57r^2 - 57r + 8 = 0
Sum = 3 / (1 - 2/9) = 3 / (7/9) = 27/7
Sum of cubes = (2/9)^3 / (1 - (2/9)^3) = 8/729 / (1 - 8/729) = 8/729 / (721/729) = 8/721
