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Question
Verify whether the following sequence is H.P.:
`1/3, 1/6, 1/9, 1/12`, ...
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Solution
`1/3, 1/6, 1/9, 1/12`, ...
Here, the reciprocal sequence is 3, 6, 9, 12 …
∴ t1 = 3, t2 = 6, t3 = 9, t4 = 12, …
∵ t2 – t1 = t3 - t2 = t4 - t3 = 3, ... constant
∴ The reciprocal sequence is an A.P.
∴ The given sequence is H.P.
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