Geometric series are really interesting in math! They're a special kind of list where you get each number by multiplying the one before it by a constant. This constant is called the common ratio.

Here’s how they work:

• First term: We call this the starting number and label it $a_1$.
• Common ratio: This is what we use to multiply, and we call it $r$.
• General form: You can find the $n^{th}$ term (which means the number in the list at position n) like this: $a_n = a_1 \cdot r^{(n-1)}$.

For example, if you start with 2 and multiply by 3:

• The sequence will look like this: 2, 6, 18, 54, ...
• The series, or the total of those numbers, would be: $2 + 6 + 18 + 54 + ...$

Geometric series are super handy and are used in many areas, especially in money-related topics!