If the p^{th} term of an A.P. is q and the q^ | vedclass

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(A) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Given $a_p =

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$p+q-r$

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(A) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n-1)d$.Given $a_p = q$,we have $a + (p-1)d = q$ $....(1)$Given $a_q = p$,we have $a + (q-1)d = p$ $....(2)$Subtracting equation $(2)$ from equation $(1)$:$(a + (p-1)d) - (a + (q-1)d) = q - p$$(p - 1 - q + 1)d = -(p - q)$$(p - q)d = -(p - q)$$d = -1$Substituting $d = -1$ in equation $(1)$:$a + (p-1)(-1) = q$$a - p + 1 = q$$a = p + q - 1$Now,the $r^{th}$ term is $a_r = a + (r-1)d$.$a_r = (p + q - 1) + (r - 1)(-1)$$a_r = p + q - 1 - r + 1$$a_r = p + q - r$

If the $p^{th}$ term of an $A.P.$ is $q$ and the $q^{th}$ term is $p,$ then its $r^{th}$ term is

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