# Weird nested sequence! $$V_{ij}$$

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.