Question

Find the 50^th term of the sequence:

`1/n, (n + 1)/n, (2n + 1)/n,..........`

Answer 1

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

t_n = a + (n – 1)d

`=> t_50 = 1/n + (50 -1)(1)`

= `1/n + 49`

So, the 50^th term is `1/n + 49`.