If the $p^{\text{th}}$,$q^{\text{th}}$,and $r^{\text{th}}$ terms of a $G.P.$ are $a$,$b$,and $c$ respectively,prove that $a^{q-r} b^{r-p} c^{p-q} = 1$.

(N/A) Let $A$ be the first term and $R$ be the common ratio of the $G.P.$
According to the given information:
$A R^{p-1} = a$
$A R^{q-1} = b$
$A R^{r-1} = c$
Now,consider the expression $a^{q-r} \cdot b^{r-p} \cdot c^{p-q}$:
$= (A R^{p-1})^{q-r} \cdot (A R^{q-1})^{r-p} \cdot (A R^{r-1})^{p-q}$
$= A^{q-r+r-p+p-q} \cdot R^{(p-1)(q-r) + (q-1)(r-p) + (r-1)(p-q)}$
Calculating the exponent of $A$:
$q-r+r-p+p-q = 0$
Calculating the exponent of $R$:
$(pq - pr - q + r) + (qr - pq - r + p) + (rp - rq - p + q) = 0$
Thus,the expression becomes:
$= A^0 \cdot R^0 = 1 \cdot 1 = 1$
Hence,the result is proved.