To find the third term of a geometric sequence, we need to follow these steps:

1. The first term $a_1 = 4$.

2. The second term $a_2 = 5.8$.

3. A geometric sequence follows the relationship: $a_n = a_1 \cdot r^{n-1}$ where $r$ is the common ratio between consecutive terms.

4. To find $r$, we can use the ratio of the second term to the first term: $r = \frac{a_2}{a_1} = \frac{5.8}{4} = 1.45$

5. Now, we can find the third term $a_3$ using the formula: $a_3 = a_1 \cdot r^2$ Substituting the values: $a_3 = 4 \cdot (1.45)^2$

Let's calculate the third term.The third term of the geometric sequence is $8.4100$, rounded to four decimal places.

Would you like further details or explanations? Here are five related questions for practice:

1. What is the fourth term of the sequence?
2. How would you find the 10th term of this geometric sequence?
3. If the first term was 3 instead of 4, what would the common ratio be?
4. How do you derive the formula for the nth term in a geometric sequence?
5. What is the sum of the first three terms of this geometric sequence?

Tip: In geometric sequences, the common ratio can be found by dividing any term by the previous one!