Question -
Answer -
LetтАЩs take┬аA┬аtobe the first term and┬аR┬аto be the common ratio of the G.P.
Then according to thequestion, we have
ARpтАУ1┬а=┬аa
ARqтАУ1┬а=┬аb
ARrтАУ1┬а=┬аc
Then,
aqтАУr┬аbrтАУp┬аcpтАУq
=┬аAqтАУr┬а├Ч┬аR(pтАУ1)(qтАУr)┬а├Ч ArтАУp┬а├Ч┬аR(qтАУ1)(rтАУp)┬а├Ч┬аApтАУq┬а├Ч┬аR(r┬атАУ1)(pтАУq)
=┬аAq┬атАУ┬аr┬а+┬аr┬атАУ┬аp┬а+┬аp┬атАУ┬аq┬а├Ч┬аR┬а(pr┬атАУ┬аpr┬атАУ┬аq┬а+┬аr)+ (rq┬атАУ┬аr┬а+┬аp┬атАУ┬аpq) +(pr┬атАУ┬аp┬атАУ┬аqr┬а+┬аq)
=┬аA0┬а├Ч┬аR0
= 1
Hence proved.