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If the A.M. between m th and n th term of an A.P. be equal to A.M. between pth and qth terms of the A.P then

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m + n = p + q

m + q = p + n

m + p = n + q

m + n + p + q =0

answer is A.

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Detailed Solution

$\frac{a_{m} + a_{n}}{2} = \frac{a_{p} + a_{q}}{2} a + (m - 1) d + a + (n - 1) d = a + (p - 1) d + a + (q - 1) d m + n - 2 = p + q - 2 \Rightarrow m + n = p + q$

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