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Question
Find the nth term and hence find the 8th term of the following H.P.s:
`1/2, 1/5, 1/8, 1/11`, ...
Solution
`1/2, 1/5, 1/8, 1/11`, ... are in H.P.
∴ 2, 5, 8, 11, … are in A.P.
∴ a = 2, d = 3
tn = a + (n – 1)d
= 2 + (n – 1)(3)
= 3n – 1
∴ nth term of H.P. is `1/(3"n" - 1)`
∴ 8th term of H.P. = `1/(3(8) - 1) = 1/23`
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