If the {p^{th}},{q^{th}} and {r^{th}} term of | vedclass

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Question

(b) Let $AR^{p-1}=a$ &hellip;..(i)

$A{R^{q - 1}} = b$ &hellip;..(ii)

and $A{R^{r - 1}} = c$ &hellip;..(iii)

So ${a^{q - r}}{b^{r - p}}{c^{p -

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(b) Let $AR^{p-1}=a$ &hellip;..(i)

$A{R^{q - 1}} = b$ &hellip;..(ii)

and $A{R^{r - 1}} = c$ &hellip;..(iii)

So ${a^{q - r}}{b^{r - p}}{c^{p - q}}$ $ = {\left\{ {A{R^{p - 1}}} \right\}^{q - r}}\left\{ {A{R^{q - 1}}} \right\}{\,^{r - p}}{\left\{ {A{R^{r - 1}}} \right\}^{p - q}}$

$ = {A^0}{R^0} = 1$.

Note : Such type of questions $i.e.$ containing terms of powers in cyclic order associated with negative sign, reduce to $1 $ mostly.

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

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