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Question

If the pth,qth,rth and sth terms of an A.P. are in G.P. then pq,qr,rs are in .........

A
A.P
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B
H.P
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C
G.P
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D
A.G.P
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Solution

The correct option is B G.P
pth,qth,rth and sth terms of an A.P. are in G.P.

Let a be first term and d be common difference of A.P. and R be common ratio of G.P.

a+(p1)d,a+(q1)d,a+(r1)d,a+(s1)d are in G.P.

R=a+(q1)da+(p1)d=a+(r1)da+(q1)d=a+(s1)da+(r1)d

Consider a+(q1)da+(p1)d=a+(r1)da+(q1)d
Subtracting 1 on both sides gives

a+(q1)da+(p1)d1=a+(r1)da+(q1)d1

(qp)da+(p1)d=(rq)da+(q1)d

R=qrpq -----(1)

Similarly,
R=rsqr -----(2)

From (1) and (2)

qrpq=rsqr

pq,qr,rs are in G.P.

Hence, option C.

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