Correct Answer - Option 1 : m + n - p

__Concept:__

nth term of A.P are a, a + d , a + 2d, .... ,a + (n - 1)d.

Tn = a_{n} = a + ( n - 1 ) d

Where a = first term and d = common difference .

__Calculation:__

Formula of general term of AP is given as;

Tn = a + ( n - 1 ) d

Given. am= n and an = m

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

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

after solving these equations

we get a = m + n - 1 and d = - 1

Now a_{p} = a + (p - 1 )d

a_{p }= m + n - 1 + ( p - 1) × - 1

= m + n - 1 - p + 1

= m + n - p