If the p^{th},q^{th},and r^{th} terms of a G. | vedclass

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(B) Let the first term of the $G.P.$ be $A$ and the common ratio be $R$.Then,the $p^{th}$,$q^{th}$,and $r^{th}$ terms are given by:$a = A R^{p-1}$  $(

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$1$

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(B) Let the first term of the $G.P.$ be $A$ and the common ratio be $R$.Then,the $p^{th}$,$q^{th}$,and $r^{th}$ terms are given by:$a = A R^{p-1}$  $(i)$$b = A R^{q-1}$  $(ii)$$c = A R^{r-1}$  $(iii)$Substituting these values into the expression $a^{q - r} b^{r - p} c^{p - q}$:$= (A R^{p-1})^{q-r} (A R^{q-1})^{r-p} (A R^{r-1})^{p-q}$$= A^{(q-r) + (r-p) + (p-q)} 	imes R^{(p-1)(q-r) + (q-1)(r-p) + (r-1)(p-q)}$$= A^0 	imes R^{(pq - pr - q + r) + (qr - pq - r + p) + (rp - rq - p + q)}$$= A^0 	imes R^0 = 1 	imes 1 = 1$.

If the $p^{th}$,$q^{th}$,and $r^{th}$ terms of a $G.P.$ are $a$,$b$,and $c$ respectively,then the value of $a^{q - r} b^{r - p} c^{p - q}$ is equal to

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