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Question

If the pth,qth and rth terms of a G.P. are a, b and c, respectively. Prove that aqrbrpcpq=1.

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Solution

LetfirsttermAandcommondifference(R)tp=atq=btr=c∣ ∣ ∣G.P.tp=ARp1=atq=ARq1=btr=ARr1=cthenaqr.brp.cpq{ARp1}qr{ARq1}rp{ARr1}pqA(qr+rp+pa).R{(p1)(q1)+(q1)(rp)+(r1)(pq)}A.R=1aqr.brp.cpq=1Proved.

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