Question
If the 2nd, 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:
-
8/5
-
4/3
-
1
-
7/4
Solution
B.
4/3
Let a be the first term and d be a common difference. Then, we have a+d, a+4d, a+8d in GP,
ie. (a +4d)2 = (a+d)(a+8d)
⇒ a2 +16d2 +8ad = a2 +8ad +ad +8d2
⇒ 8d2 = ad
8d =a [∴ d≠0]
Now, common ratio,
