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Question
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.
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