# Verify whether the following sequences are H.P. : 13,15,17,19, ... - Mathematics and Statistics

Sum

Verify whether the following sequence is H.P.:

1/3, 1/5, 1/7, 1/9, ...

#### Solution

1/3, 1/5, 1/7, 1/9, ...
Here, the reciprocal sequence is 3, 5, 7, 9, …
∴ t1 = 3, t2 = 5, t3 = 7, …
∵ 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. (i) | Page 60