Let a is first term and d is the common difference of the Ap

Now given m^th term = n

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

=> a = n - (m-1)d ............1

Again given n^th term = m

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

=> a = m - (n-1)d ............2

From eqaution 1 and 2, we get

      m - (n-1)d = n - (m-1)d

=> m - nd -d = n - md - d

=> m - n = -md - d + nd + d

=> m - n = (n-m)d

=> d = (m-n)/(n-m)

=> d = -(m-n)/(m-n)

=> d = -1

from eqaution 2, we get

a = m - (n-1)*(-1)

=> a = m + (n-1) 

=> a = m + n -1

Now, p^th term = a + (p-1)d

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

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

                    = m + n -1 - p + 1

                    = m + n - p 

So, p^th term = m + n - p