Question

The nth term of the A.P. (1+√3), (1+2√3), (1+3√3) is

Answer 1

mn.................

....

....

....

Answer 2

Given,

A.P. = (1+√3), (1+2√3), (1+3√3)

To Find,

The nth term of the A.P. =?

Solution,

We can solve the question using the following steps:

The first term, $a = 1 + \sqrt{3}$

The nth term $=$ $T_{n}$

Common difference, $d = (1 + 2\sqrt{3} ) - (1 + \sqrt{3}) = \sqrt{3}$

We know,

$T_{n} = a + (n - 1)d$

Substituting the given values,

$T_{n} = (1 + \sqrt{3}) + (n - 1)\sqrt{3}$

     $= 1 + \sqrt{3} + n\sqrt{3} - \sqrt{3}$

     $= 1 + n\sqrt{3}$

Hence, the nth term of the A.P. is $1 + n\sqrt{3}$.