Question

three numbers form an gp.if the middle term is doubled,then the new numbers are in ap.find the common ratio of the gp

Answer 1

let the three numbers be a, ar and ar^2
when middle is doubled i.e. it becomes 2ar
now the new numbers( a, 2ar and ar^2 ) are in ap

i.e. 2ar-a = ar^2 - 2ar
4ar= ar^2 + a
4ar= a(r^2 +1)
4r = r^2 + 1
r^2 -4r+1 =0
now u can solve it for r by the quadratic equation method....hope it will hlp