Let the G.P. be a,ar,ar2 and termss of A.P are A + d, A + 4d , A + 8d then
ar2−ar
ar−a
=
(A+8d)−(A+4d)
(A+4d)−(A+8d)
=
4
3
⇒r=
4
3
Alternate Solution: Let Ap is a,a + d,a + 2d 2nd,5th and 9th terms a + d,a + 4d,a + 8d are in G.P ⇒(a+4d)2=(a+d)(a+8d) ⇒d(8d−a)=0⇒8d=a as d≠0 Hence common ratio of GP