Correct Answer - Option 1 : m + n - p
Concept:
nth term of A.P are a, a + d , a + 2d, .... ,a + (n - 1)d.
Tn = an = 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 ap = a + (p - 1 )d
ap = m + n - 1 + ( p - 1) × - 1
= m + n - 1 - p + 1
= m + n - p