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

a=pth term =AR(p−1)

b=qth term =AR(q−1)

c=rth term =AR(r−1)

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

a(q−r).b(r−p).c(p−q)

=[AR(p−1)](q−r).[AR(q−1)](r−p).[AR(r−1)](p−q)

=A(q−r)R(p−1)(q−r).A(r−p)R(q−1)(r−p).A(p−q)R(r−1)(p−q)

=A0R0=1

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