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Verify whether the following sequence is H.P.: 17,19,111,113,115, ... - Mathematics and Statistics

Sum

Verify whether the following sequence is H.P.:

`1/7, 1/9, 1/11, 1/13, 1/15`, ...

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Solution

`1/7, 1/9, 1/11, 1/13, 1/15`, ...
Here, the reciprocal sequence is

7, 9, 11, 13, 15,....

∴ t1 = 7, t2 = 9, t3 = 11, t4 = 13, …
∵ t2 – t1 = t3 – t2 = t4 – t3 = 2, constant
∴ The reciprocal sequence is an A.P.
∴ The given sequence is 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 1. (iii) | Page 60
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