**Solution:**

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

According to the given information,

*AR**p*–1 = *a*

*AR**q*–1 = *b*

*AR**r*–1 = *c*

*a*^{q–r} *b*^{r–p} *c*^{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*)

= *Aq* – *r* + *r* – *p* + *p* – *q* × *R* (*pr* – *pr* – *q* + *r*) + (*rq* – *r *+ *p* – *pq*) + (*pr* – *p* – *qr* + *q*)

= *A*0 × *R*0

= 1

Thus, the given equation is proved.