Here is how to fill in the blanks using the given list:

1. A sequence where each term is multiplied by a constant to obtain the next term is called a geometric series.

2. The common ratio of a geometric series is the constant factor between consecutive terms.

3. The first term in a geometric series is represented by the variable a.

4. If the common ratio $r$ is greater than 1, the terms of the geometric series increase exponentially.

5. A series that has a definite number of terms is called a finite geometric series.

6. The sum of a finite geometric series can be found using the number of terms $n$, the first term $a$, and the common ratio $r$.

7. When the common ratio $r$ is less than 1, the terms of the geometric series decrease as $n$ increases.

8. If $|r|$ is less than 1, the geometric series will converge to a finite value.

Do you need any more details or have other questions?

Here are 5 related questions:

1. How does a finite geometric series differ from an infinite one?
2. What conditions must be met for a geometric series to converge?
3. How can the common ratio affect the sum of a geometric series?
4. What happens if the common ratio is exactly 1 in a geometric series?
5. How does the concept of geometric series apply in calculating interest?

Tip: The common ratio $r$ plays a critical role in determining the behavior of a geometric series—whether it increases, decreases, or converges!