Let T r be the rth term of an A.P. whose first term is a and common difference is d . If for some positive integers m , n , m  = n , T m = n 1 and T n = m 1 , then a − d equals

Question

Let T r ​ be the rth term of an A.P. whose first term is a and common difference is d . If for some positive integers m , n , m  = n , T m ​ = n 1 ​ and T n ​ = m 1 ​ , then a − d equals

TestHub · Accepted Answer

T m ​ = n 1 ​ = a + ( m − 1 ) d and T n ​ = m 1 ​ = a + ( n − 1 ) d from (1) and (2) we get a = mn 1 ​ , d = mn 1 ​ Hence a − d = 0

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