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Question
Verify whether the following sequence is H.P.:
`1/7, 1/9, 1/11, 1/13, 1/15`, ...
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.
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