Answer :


Let the first term be a and the common ratio be R.


According to the question,


ap = x.


aq = t


ar = z.


We know that an = aRn-1


ap = aRp-1= x


aq = aRq-1= y


ar = aRr-1= z


xq-r = (aRp-1)q-r


yr-p = (aRq-1)r-p


zp-q = (aRr-1)p-q


Multiplying the above three equations we get


xq-r.yr-p.zp-q = (aq-r.Rpq-pr-q+r). (ar-p.Rrq-pq-r+p). (ap-q.Rpr-qr-p+q)


=(aq-r+r-p+p-q.Rpq-pr-q+r+rq-pq-r+p+pr-qr-p+q)


= (a0.R0)


= 1.


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