Question

Find the 100^th term of the sequence:

`sqrt(3), 2sqrt(3), 3sqrt(3),..........`

Answer 1

The given A.P is `sqrt(3), 2sqrt(3), 3sqrt(3),..........`

Now,

`2sqrt(3) - sqrt(3) = sqrt(3)`

`3sqrt(3) - 2sqrt(3) = sqrt(3)`, etc.

Hence, the given sequence is an A.P. with first term `a = sqrt(3)` and common difference `d = sqrt(3)`.

The general term of an A.P. is given by

t_n = a + (n – 1)d

`=> t_100 = sqrt(3) + (100 - 1) xx  sqrt(3)`

= `sqrt(3) + 99sqrt(3)`

= `100sqrt(3)`

So, the 100^th term is `100sqrt(3)`.