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.