The problem asks to find the 5th term, $a_5$, of a geometric sequence given the first term, $a_1 = 3$, and the common ratio, $r = 6$.

The formula for the $n$-th term of a geometric sequence is: $a_n = a_1 \cdot r^{n-1}$

Substituting the given values: $a_5 = 3 \cdot 6^{5-1} = 3 \cdot 6^4$

Now calculate: $6^4 = 1296$ $a_5 = 3 \cdot 1296 = 3888$

Thus, the 5th term ($a_5$) is: $\boxed{3888}$

Let me know if you'd like a step-by-step breakdown of these calculations or further clarifications.

Related Questions:

1. What is the formula for the sum of the first $n$ terms in a geometric sequence?
2. How does the common ratio $r$ affect the growth of a geometric sequence?
3. What happens if $r$ is less than 1 in a geometric sequence?
4. How can you verify your calculations when solving for $a_n$?
5. Can a geometric sequence have a negative common ratio? If so, how does it behave?

Tip:

Always double-check your calculations, especially when working with powers and large numbers!