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

$n+m-p$

Finding pth term.
Given, am=n and an=m, where m≠n
Let d= common difference and a= first term
We have,
am=a+(m−1)d=n⋯(i)
an=a+(n−1)d=m⋯(ii)

Subtracting equation (i) and (ii)
⇒(m−1)d−(n−1)d=n−m
⇒md−d−nd+d=n−m
⇒(m−n)d=n−m
⇒d=−1 (Substitute in equation (i))
a+(m−1)(−1)=n
⇒a=n+(m−1)=n+m−1

Now, pth term
ap=a+(p−1)d
=(n+m−1)+(p−1)(−1)
=n+m−p
Hence, the pth term is n+m−p