1.

Insert three harmonic between `(1)/(12) and (1)/(20)`.

Answer» After inserting the harmonic means, let the harmonic progression be,
`(1)/(a) , (1)/(a+d) , (1)/(a+2d), (1)/(a+3d), (1)/(a+4d)`
Given, `(1)/(a) = (1)/(12) and (1)/(a+4d) = (1)/(20)rArr a = 12 and d = 2`
`therefore ` The required harmonic means are `(1)/(14), (1)/(16) and (1)/(18)`.


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