If the 2nd, 5th and 9th terms of a non-constant AP are in GP, then the common ratio of this GP is
43
Let a be the first term and d be the common difference. Then, we have
a+d,a+4d,a+8d in GP
i.e., (a+4d)2=(a+d)(a+8d)
⇒a2+16d2+8ad=a2+8ad+ad+8d2
⇒8d2=ad
⇒8d=a [∵d≠0]
Now, common ratio,
r=a+4da+d=8d+4d8d+d=12d9d=43