Q7 of 167 Page 19

If n A.M.s are inserted between two numbers, prove that the sum of the means equidistant from the beginning and the end is constant.

Let a and b be the first and last terms and


The series be a, A1, A2, A3, ........, An, b


So We know, Mean


Mean of A1 and An =


A1 = a + d


An = a - d


Therefore, AM


AM between A2 and An-1


Similarly, it is (a + b)/2 for all such numbers, which is constant


Hence, AM = (a + b)/2


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