If a, b, c are the p^{th}, q^{th} and r^{th} | vedclass

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(A) Let the first term of the $G.P.$ be $A$ and the common ratio be $R$.Then,$a = A R^{p-1}$,$b = A R^{q-1}$,and $c = A R^{r-1}$.Substituting these in

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(A) Let the first term of the $G.P.$ be $A$ and the common ratio be $R$.Then,$a = A R^{p-1}$,$b = A R^{q-1}$,and $c = A R^{r-1}$.Substituting these into the expression:$\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q = \left( \frac{A R^{r-1}}{A R^{q-1}} \right)^p \left( \frac{A R^{q-1}}{A R^{p-1}} \right)^r \left( \frac{A R^{p-1}}{A R^{r-1}} \right)^q$$= (R^{r-q})^p (R^{q-p})^r (R^{p-r})^q$$= R^{pr - pq + qr - pr + pq - qr}$$= R^0 = 1$.

If $a, b, c$ are the $p^{th}, q^{th}$ and $r^{th}$ terms of a $G.P.$,then $\left( \frac{c}{b} \right)^p \left( \frac{b}{a} \right)^r \left( \frac{a}{c} \right)^q$ is equal to

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