Sum

Insert two numbers between `1/7 and 1/13` so that the resulting sequence is a H.P.

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#### Solution

Let the required numbers be `1/"H"_1 and 1/"H"_2`.

∴ `1/7, 1/"H"_1, 1/"H"_2, 1/13` are in H.P.

∴ 7, H_{1}, H_{2} and 13 are in A.P.

∴ t_{1} = a = 7 and t_{4} = a + 3d = 13

∴ 7 + 3d = 13

∴ 3d = 6

∴ d = 2

∴ H_{1} = t_{2} = a + d = 7 + 2 = 9

and H_{2} = t_{3} = a + 2d = 7 + 2(2) = 11

∴ `1/9 and 1/11` are the required numbers to be inserted between `1/7 and 1/13` so that the resulting sequence is a H.P.

Concept: Harmonic Progression (H. P.)

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