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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.

Solution
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Let A be the first term and R be the common ratio. Then,

a=pth term =AR(p1)

b=qth term =AR(q1)

c=rth term =AR(r1)

Substituting values of a,b & c, we get,

a(qr).b(rp).c(pq)

=[AR(p1)](qr).[AR(q1)](rp).[AR(r1)](pq)

=A(qr)R(p1)(qr).A(rp)R(q1)(rp).A(pq)R(r1)(pq)

=A0R0=1

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