等差等比數列問題

Let a = area covered by flowers in 1 week and
A = area of the garden.
Area covered by flowers in the 2nd week = 2a
Area covered by flowers in the 3rd week = 2 x (2a) = a(2^2)
So area covered in 16 weeks = a(2^15) = area of the garden = A
Let n = no. of weeks to cover 1/8 of the garden
so a[2^(n - 1)] = A/8 = a(2^15)/8
2^(n - 1) = 2^15/8 = 2^15/2^3 = 2^12
n - 1 = 12
n = 13.
So it takes 13 weeks to cover 1/8 of the garden.