Among the following the correct statement is

A) Sum of n terms of the list of numbers $\sqrt{2},\sqrt{8},\sqrt{18},\sqrt{32},\cdots$  is $\frac{n\left(n+1\right)}{\sqrt{2}}$

B) The common difference of the A.P $3n+2$  given by is 3.

C) The sum of the A.P $\left(-5\right),\left(-8\right),\left(-11\right),\cdots \left(-230\right)$  is $-8930$

Option(A):Given A.P is $\sqrt{2},2\sqrt{2},3\sqrt{2},4\sqrt{2},\cdots$

$S_n=\frac{n}{2}\left[2\sqrt{2}+\left(n-1\right)\left(\sqrt{2}\right)\right]$

$=\frac{n}{2}\times \sqrt{2}\left[2+n-1\right]=\frac{n}{\sqrt{2}}\left[n+1\right]$

Option(B): Since, $a_n=3n+2$  here, $a_1=3\left(1\right)+2=5,a_2=3\left(2\right)+2=8$

$\therefore$ Common difference $=a_2-a_1=3$

Option(C): Given A.P is $\left(-5\right),\left(-8\right),\left(-11\right),\cdots ,\left(-230\right)$

$\therefore a_n=a+\left(n-1\right)\left(-3\right)$

$\Rightarrow -230=-5+\left(n-1\right)\left(-3\right)$

$\Rightarrow \frac{-225}{-3}=\left(n-1\right)$

$\Rightarrow n=75+1=76$

$\Rightarrow S_n=\frac{76}{2}\left(\left(-5\right)+\left(-230\right)\right)=-8930$

Option(D):