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Question

If the 2nd, 5th and 9th terms of a non-constant AP are in GP, then the common ratio of this GP is

A
43
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B
1
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C
85
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D
74
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Solution

The correct option is A 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 [d0]
Now, common ratio,
r=a+4da+d=8d+4d8d+d=12d9d=43

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