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InterviewSolution
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6. Prove that the sum of n A.M's between a and b is n times the A.M. between a and b.of m A M's between any two numbers is to the sum of n A.M's |
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Answer» Let n a.m, between a,b are a1,a2,a3,............ana,a1,a2,a3,.............an,bsum of n a.m.Sn = n[2a1 + (n-1)d]/2 ----------(1)a.m. of a,b is (a+b)/2b = a+(n+1)da.m. = [2a+(n+1)d]/2 -------------(2)a1 = a+d put in (1)Sn = n[2a + 2d + (n-1)d]/2 = n[2a+(n+1)d]/2 ------------(3)from equation (2) & (3)Sn = n*a.m.where d = common difference of a.p. |
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