If the A.M. between ` p^(th) and q^(th)` terms of an A.P. , be equal to the A.M., between ` m^(th) and n^(th) `
terms of the A.P. , then show that ` p + q = m + n ` .

Explanation

A.M. between ` p^(th) and q^(th) ` term of A.P. `= (a + (p-1) d + a + (q - 1)d)/(2) = (2a (p +q -2)d)/(2)`
Similarly , A.M. between ` m^(th) and n^(th) ` term of A.P. `= (2a + (m+ n - 2)d)/(2) `
Given , `(2a + (p + q - 2)d) /(2) = (2a + (m + n - 2)d)/(2) `
`rArr P + q = m + n `