Weird nested sequence! $V_{ij}$

Number Theory Level 4

Consider the sequence $3,18,243,...n×3^{2^{n-1}}$

If this sequence is enclosed in nested square roots upto infinite terms i.e. if

$\sqrt{3+\sqrt{18+\sqrt{243+...}}}=k$ ,

Find the value of $\left\lceil{k}\right\rceil$ .

Note:

This problem is similar to the below problem.