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

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Question

(c) Suppose that first term and common difference of $A.P.$'s are $A$ and $D$ respectively.

Now, ${p^{th}}$ term $ = A + (p - 1)D = a$ &hellip;

Vedclass · Accepted Answer

$0$

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(c) Suppose that first term and common difference of $A.P.$'s are $A$ and $D$ respectively.

Now, ${p^{th}}$ term $ = A + (p - 1)D = a$ &hellip;..$(i)$

${q^{th}}$term $ = A + (q - 1)D = b$ ......$(ii)$

and ${r^{th}}$ term $ = A + (r - 1)D = c$ &hellip;..$(iii)$

So, $a(q - r) + b(r - p) + c(p - q)$

$ = a\left\{ {\frac{{b - c}}{D}} \right\} + b\left\{ {\frac{{c - a}}{D}} \right\} + c\left\{ {\frac{{a - b}}{D}} \right\}$

$ = \frac{1}{D}(ab - ac + bc - ab + ca - bc) = 0$.

If the ${p^{th}},\;{q^{th}}$ and ${r^{th}}$ term of an arithmetic sequence are $a , b$ and $c$ respectively, then the value of $[a(q - r)$ + $b(r - p)$ $ + c(p - q)] = $

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