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Question

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

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Solution

Given : pth,qth,rth,sth are in A.P.
With the usual notation we have
a+(p1)da+(q1)d=a+(q1)da+(r1)d=a+(r1)da+(s1)d;
each of these ratios
={a+(p1)d}{a+(q1)d}{a+(q1)d}{a+(r1)d}={a+(q1)d}{a+(r1)d}{a+(r1)d}{a+(s1)d}
pqqr=qrrs.
Hence pq,qr,rs are in G.P.

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