Here, a_m=n and a_n=m

∴ a+(m-1)d=n and a+(n-1)d=m_______(1)

Subtracting above two equation we get

a +(m-1)d-a-(n-1)d=n-m

∴ md-d-nd+d=n-m

∴ d(m-n)=n-m

∴ d=-1

Substituting d=-1 in a+(m-1)d=n we get

∴ a+(m-1)(-1)=n

∴ a-m+1=n

∴ a=m+n-1

Now, p^th term is given by a_p=a+(p-1)d

=m+n-1+(p-1)(-1)

=m+n-1-p+1

=m+n-p