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Question
Insert two numbers between `1/7 and 1/13` so that the resulting sequence is a H.P.
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, H1, H2 and 13 are in A.P.
∴ t1 = a = 7 and t4 = a + 3d = 13
∴ 7 + 3d = 13
∴ 3d = 6
∴ d = 2
∴ H1 = t2 = a + d = 7 + 2 = 9
and H2 = t3 = 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.
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