the first three terms of a GP are the first, fourth and tenth terms of an AP. given that the first term is 6 and that all the terms of a GP are different, find the common ratio.

Answer 1

a = 6
ar = a+3d
ar^2 = a+9d
so,
d = (ar-a)/3

ar^2 = a+9a(r-1)/3
r^2 = 1+3r-3
r^2-3r+2 = 0
r = 1 or 2

since the GP terms are different, r=2 and d=2 and the sequences are

6,12,24
6,8,10,12,14,16,18,20,22,24

Answer 2

The first ,second and sixth term of an ap and the first three terms of a gp .findthe possible values of the common ratio of the gp