Here,
am = n and
an = 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,
pth term is given by ap = a+(p-1)d
= m+n-1+(p-1)(-1)
= m+n-1-p+1
= m + n - p