lf a, b, c are pth, qth and rth terms of a GP, then (q - r) log a + (r - p) log b + (p - q) log c is equal to

Let A and R be the first term and common ratio of the given GP. Then, a = ARP-1⇒log⁡a=log⁡A+(p−1)log⁡R-----isimilarly, log⁡b=log⁡A+(q−1)log⁡R----iiand log⁡c=log⁡A+(r−1)log⁡R-----iiinow , (q - r) log a + (r - p) log b + (p - q) log c=(q−r){log⁡A+(p−1)log⁡R}+(r−p){log⁡A+(q−1)log⁡R}+(p−q){log⁡A+(r−1)log⁡R}  =log⁡A[q−r+r−p+p−q]+log⁡R[p(q−r)+q(r−p)+r(p−q)−(q−r)−(r−p)−(p−q)]  =log⁡A⋅0+log⁡R⋅0=0