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Question
Verify whether the following sequence is H.P.
`5, 10/17, 10/32, 10/47, ...`
Solution
`5, 10/17, 10/32, 10/47, ...`
Here, the reciprocal sequence is `1/5, 17/10, 32/10, 47/10, ...`
∴ t1 = `1/5`, t2 = `17/10`, t3 = `32/10`, t4 = `47/10`, ...
∵ t2 – t1 = t3 – t2 = t4 – t3 = `3/2` , constant
∴ The reciprocal sequence is an A.P.
∴ The given sequence is a H.P.
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