Write a formula for the $\mathrm{nth}$ term of the following geometric sequence. Then use the formula for $a_n$ to find $a_6$, the 6 th term of the sequence.
$4,16,64,\dots$
Enter a formula for the $\mathrm{nth}$ term of the geometric sequence.
$$a_n=◻\cdot (◻{)}^{n-1}$$

Step 1 ：The given sequence is a geometric sequence. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In this case, the common ratio is 4 (16/4 = 4, 64/16 = 4).

Step 2 ：The formula for the nth term of a geometric sequence is given by: $a_n=a_1\cdot r^{(n-1)}$ where: $a_n$ is the nth term of the sequence, $a_1$ is the first term of the sequence, r is the common ratio, n is the term number.

Step 3 ：In this case, $a_1$ = 4 and r = 4. So, the formula for the nth term of the sequence is: $a_n=4\cdot 4^{(n-1)}$

Step 4 ：Now, we can use this formula to find the 6th term of the sequence. $a_1$ = 4, r = 4, n = 6, $a_n$ = 4096

Step 5 ：Final Answer: The 6th term of the sequence is $\boxed{{\displaystyle 4096}}$