ther is an infinite series with geometric progression, 1st term is the sum of 2nd and 3rd terms, then find the common ratio....

let geometric series is , a , ar  , ar² , ar² ................ infinity

first term is sum of 2nd & third term

a = ar + ar²

r²+r-1 = 0  or        ................1

ax²+bx+c           ............2

this is quadratic equation & its solution is given by dharacharya rule

x = [-b+(-)(b²-4ac)^1/2]/2a

a = 1 , b = 1 , c=-1                (on comparing both equations)

x = (root5 - 1)/2     or  -(root5 + 1)/2