To find the first five terms of the geometric sequence, we use the formula for the $n$th term of a geometric sequence:

$a_n = a_1 \cdot r^{n-1}$

Given:

• $a_1 = 4$
• $r = 3$

Now, we can calculate the first five terms:

1. $a_1 = 4 \cdot 3^{0} = 4$
2. $a_2 = 4 \cdot 3^{1} = 12$
3. $a_3 = 4 \cdot 3^{2} = 36$
4. $a_4 = 4 \cdot 3^{3} = 108$
5. $a_5 = 4 \cdot 3^{4} = 324$

So, the first five terms of the geometric sequence are 4, 12, 36, 108, 324.

Would you like more details or have any questions?

Here are five related questions to consider:

1. What is the formula to find the $n$th term in a geometric sequence?
2. How do you determine the sum of the first $n$ terms in a geometric sequence?
3. What happens to the sequence if the common ratio $r$ is a fraction?
4. Can you find the 10th term of this sequence using the same formula?
5. How would the sequence change if the common ratio was negative?

Tip: In a geometric sequence, each term is found by multiplying the previous term by a constant called the common ratio.