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Insert two numbers between 17and113 so that the resulting sequence is a H.P. - Mathematics and Statistics

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, 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.

Concept: Harmonic Progression (H. P.)
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 4 Sequences and Series
Exercise 4.4 | Q 6 | Page 60
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