Find a formula for the $n$th term of the sequence. \[ \sqrt{6}, \quad \sqrt{6 \sqrt{6}}, \quad \sqrt{6 \sqrt{6 \sqrt{6}}}, \quad \sqrt{6 \sqrt{6 \sqrt{6 \sqrt{6}}}}, \ldots \] [Hint: Write each term as a power of 6.] \[ a_{n}= \]

Step 1 ：The sequence is a nested radical sequence. The first term is \(\sqrt{6}\), the second term is \(\sqrt{6 \sqrt{6}}\), the third term is \(\sqrt{6 \sqrt{6 \sqrt{6}}}\), and so on. We can see that each term is the square root of 6 times the previous term.

Step 2 ：We can write each term as a power of 6. The first term is \(6^{1/2}\), the second term is \(6^{1/2 + 1/4}\), the third term is \(6^{1/2 + 1/4 + 1/8}\), and so on.

Step 3 ：So, we can see that the nth term of the sequence is \(6^{1/2 + 1/4 + 1/8 + \ldots + 1/2^n}\).

Step 4 ：The nth term of the sequence is \(6^{\sum_{i=1}^{n} \frac{1}{2^{i}}}\).

Step 5 ：\(\boxed{a_{n}=6^{\sum_{i=1}^{n} \frac{1}{2^{i}}}}\)