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(D) Let the first term be $a$ and the common difference be $d$.Given that the $p^{th}$ term is $q$:$a + (p - 1)d = q$  --- $(i)$Given that the $q^{th}

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(D) Let the first term be $a$ and the common difference be $d$.Given that the $p^{th}$ term is $q$:$a + (p - 1)d = q$  --- $(i)$Given that the $q^{th}$ term is $p$:$a + (q - 1)d = p$  --- $(ii)$Subtracting $(ii)$ from $(i)$:$(a + (p - 1)d) - (a + (q - 1)d) = q - p$$(p - 1 - q + 1)d = q - p$$(p - q)d = -(p - q)$$d = -1$Substituting $d = -1$ into $(i)$:$a + (p - 1)(-1) = q$$a - p + 1 = q$$a = p + q - 1$The $(p + q)^{th}$ term is given by:$T_{p+q} = a + (p + q - 1)d$$T_{p+q} = (p + q - 1) + (p + q - 1)(-1)$$T_{p+q} = p + q - 1 - p - q + 1 = 0$

If the $p^{th}$ term of an arithmetic progression is $q$ and its $q^{th}$ term is $p$,then what is its $(p + q)^{th}$ term?

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