there are 9 adjacent sectors in a circle and their total area is 1/3 rd the area of the circle. if the area?

Question

of the g th sector is 3 times the area of the (g-1)th sector, for g = 2,3,4,..9 . what is the approx. angle of the 9 th sector in radians ?

how to solve this ques.
ans given in book is 4pie / 9

Answer 1

if total area is 1/3 the area of a circle the the included angle is 1/3 of the total angular measure of a circle or 2pi/3 radians.
let g = angle of first sector.
g(3^0 +3^1 +3^2 +3^3 +3^4 +3^5 +3^6 +3^7 +3^8) =2pi/3
sum the series and solve for g

the are of 9th sector is then g(3^8)