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Question

If pth,qth,rth and sth, terms of an A.P are in G.P, then the show that (pq),(qr),(rs) are also in G.P ?

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Solution

ap=a+(p1)d;aq=a+(q1)d;ar=a+(r1)d;as=a+(s1)d;A/Qpth,qth,rth,sthtermareinG.Paqap=araq=asarforaqap=araqaqap1=araq1aqap=araqaqapputtingthevalueoftermwegetaqap=(a+(r1)d)(a+(q1)d)(a+(q1)d)(a+(p1)d)=qrpq(1)similarlyforaraq=asararaq=rsqr(2)from(1)and(2)wecometoknow(pq),(qr)and(rs)areinG.P

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