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

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(c) Let first term =$ A $ and common difference =$ D$

$	herefore a = A + (p - 1)D$, $b = A + (q - 1)D$, $c = A + (r - 1)D$

$\left| {\begin{arra

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(c) Let first term =$ A $ and common difference =$ D$

$	herefore a = A + (p - 1)D$, $b = A + (q - 1)D$, $c = A + (r - 1)D$

$\left| {\begin{array}{*{20}{c}}{\,a\,\,\,}&{p\,\,\,}&{1\,}\{\,b\,\,\,}&{q\,\,\,}&1\{\,c\,\,\,}&{r\,\,\,}&1\end{array}} ight| = \left| {\begin{array}{*{20}{c}}{\,A + (p - 1)D\,\,\,}&{p\,\,\,}&{1\,}\{A + (q - 1)D\,\,\,}&{q\,\,\,}&1\{A + (r - 1)D\,\,\,}&{r\,\,\,}&1\end{array}} ight|$

Operate ${C_1} 	o {C_1} - D{C_2} + D{C_3}$

$ = \,\left| {\begin{array}{*{20}{c}}{\,A\,\,}&{p\,\,}&{1\,}\{\,A\,\,}&{q\,\,}&1\{\,A\,\,}&{r\,\,}&1\end{array}} ight| = A\left| {\begin{array}{*{20}{c}}{\,\,1}&{\,\,p}&{\,\,1\,}\{\,1}&q&1\{\,1}&r&1\end{array}} ight| = 0$.

If $a,b,c$ are respectively the ${p^{th}},{q^{th}}{r^{th}}$terms of an $A.P.,$ the $\left| {\,\begin{array}{*{20}{c}}a&p&1\\b&q&1\\c&r&1\end{array}\,} \right| = $

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