Answer:
Let a and b be the first and last terms
The series be a, A1, A2, A3, …….., An, b
Mean = (a+b)/2
Mean of A1 and An = (A1 + An)/2
A1 = a+d
An = a – d
AM = (a+d+b-d)/2
AM = (a+b)/2
AM between A2 and An-1 = (a+2d+b-2d)/2
=> (a+b)/2
(a + b)/2 is constant for all such numbers
Hence, AM = (a + b)/2