If the pth, qth and rth terms of a GP be a, b, c respectively, prove that

a^(q-r).b^(r-p).c^(p-q)=1;

where ^=raised to the power

Let A and R be the first term and common ratio of G.P. respectively.

*n* ^{th} term of G.P., *a _{n} *= AR

^{n }^{– 1}

*p* ^{th} term of G.P. = *a*

∴ AR* ^{p} *

^{ – 1}=

*a*...(1)

*q* ^{th} term of G.P. = *b*

∴ AR* ^{q} *

^{ – 1}=

*b*...(2)

*r* ^{th }term of G.P. = *c*

∴ AR* ^{r} *

^{ – 1}=

*c*...(3)

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