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Question

# if pth,qth,rth and sth terms of an A.P. be in G.P., then (p - q),(q - r),(r - s) will be in

A

G.P

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B

A.P

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C

H.P

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D

None of these

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Solution

## The correct option is A G.P If a and d be the first term and common duifference of tha A.P. Then Tp = a + (p - 1)d, Tq = a + (q - 1)d and Tr = a+(r - 1)d. If Tp,Tq,Tr are in G.P. Then its common ratio R = TqTp = TrTq = Tq−TrTp−Tq = [a+(q−1)d]−[a+(r−1)d][a+(p−1)d]−[a+(q−1)d] = q−rp−q Similarly, we can show that R =q−rp−q = r−sq−r Hence (p - q), (q - r),(r - s) be in G.P.

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