Question

the next term of the series √3,√12,√27, ...is?

Answer 1

Heya!!

Here's ur answer..

First term =
$\sqrt{3}$

Second term =

$\sqrt{12} = 2 \sqrt{3}$

So, common difference = second term - first term.

Common difference =
$2 \sqrt{3} - \sqrt{3} = \sqrt{3}$


So, next terms are :
$\sqrt{27} = 3 \sqrt{3} \\ \\ next \: term \: \\ 3 \sqrt{3} + \sqrt{3} = 4 \sqrt{3} \\ \\ next \: is \: 5 \sqrt{3} \\ \\ \\ so \\ \\ answer \: is \: 4\sqrt{3}$


Hope it helps!!

Thank you ^_^

Answer 2

It is in Arithmetic series , so
d = T2 - T1
d = √12 - √3
d = √4×√3 - √3
d = √3(√4-1)
d = √3(2-1)
d = √3(1)
d = √3

so the next term is
√27 + √3
√9×√3 + √3
√3(√9+1)
√3(3+1)
√3(4)
4√3