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In an AP , if mth term is n and nth term is m where n is not equal to  m , then find pth term ?
1. m + n - p
2. m + n + p
3. m - n - p
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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 a= 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 

a= m + n - 1 + ( p - 1) × - 1

= m + n - 1 - p + 1 

= m + n - p

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