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Question

If a, 1, c are in A.P and a, 2, c are in G.P, then for a, b, c to be H.P the value of b = __


Solution

a, b, c are in H.P.

b is H.M. =  2aca+c                    -------------(1)

as a, 1, c are in A.P.    a+c2 = 1

                                       a + c = 2            -------------(2)

 as a, 2, c are in G.P.   22 = ac

                                         ac = 4             ---------------(3)

substituting (2) & (3) in (1), 

 b =   2(4)2 = 4


Mathematics

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