Question

In an AP , if m^th term is n and n^th term is m where n is not equal to  m , then find p^th term ?
1. m + n - p
2. m + n + p
3. m - n - p
4. 0

Answer 1

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