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Question
Find the 50th term of the sequence:
`1/n, (n + 1)/n, (2n + 1)/n,..........`
Solution
The given sequence is `1/n, (n + 1)/n, (2n + 1)/n,..........`
Now,
`(n + 1)/n - 1/n = (n + 1 - 1)/n = n/n = 1`
`(2n + 1)/n - (n + 1)/n = (2n + 1 - n - 1)/n = n/n = 1`, etc.
Hence, the given sequence is an A.P. with first term a = `1/n` and common difference d = 1.
The general term of an A.P. is given by
tn = a + (n – 1)d
`=> t_50 = 1/n + (50 -1)(1)`
= `1/n + 49`
So, the 50th term is `1/n + 49`.
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