two consecutive terms of a GP are the 2nd ,4th and 7th terms of an A.P respectively.find the common ration of the GP

Answer 1

so the GP terms are:
a+d, a+3d, and a+6d

(a+3d)/(a+d) = (a+6d)/(a+3d)

(a+6d)(a+d) = (a+3d)^2
a^2 + 7ad + 6d^2 = a^2 + 6ad + 9d^2
ad = 3d^2
divide by d
a = 3d

common ratio :
r = (a+3d)/(a+d)
= 6d/(4d)
= 3/2