In an A.P.,if the m^{text{th}} term is n and | vedclass

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(A) Let the first term be $a$ and the common difference be $d$.We are given:$a_m = a + (m - 1)d = n$  --- $(1)$$a_n = a + (n - 1)d = m$  --- $(2)$Subt

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$n+m-p$

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(A) Let the first term be $a$ and the common difference be $d$.We are given:$a_m = a + (m - 1)d = n$  --- $(1)$$a_n = a + (n - 1)d = m$  --- $(2)$Subtracting $(2)$ from $(1)$:$(a + (m - 1)d) - (a + (n - 1)d) = n - m$$(m - 1 - n + 1)d = n - m$$(m - n)d = -(m - n)$Since $m 
eq n$,we can divide by $(m - n)$:$d = -1$Substituting $d = -1$ into $(1)$:$a + (m - 1)(-1) = n$$a - m + 1 = n$$a = n + m - 1$Now,the $p^{	ext{th}}$ term is given by:$a_p = a + (p - 1)d$$a_p = (n + m - 1) + (p - 1)(-1)$$a_p = n + m - 1 - p + 1$$a_p = n + m - p$

In an $A.P.$,if the $m^{\text{th}}$ term is $n$ and the $n^{\text{th}}$ term is $m$,where $m \neq n$,find the $p^{\text{th}}$ term.

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