To find the sum of a specific geometric series, you can use a simple formula:

S_n = a × (1 - r^n) / (1 - r)

Let's break down what this means:

• S_n is the total of the first n terms.
• a is the first number in the series.
• r is the common ratio, or how much you multiply each term to get the next one.
• n is how many terms you want to add together.

Example:

Let's look at this series: 2, 6, 18, 54, ...

In this case:

• The first term (a) is 2.
• The common ratio (r) is 3 (since 6 divided by 2 is 3).
• The number of terms (n) is 4.

Now, we can use the formula:

S_4 = 2 × (1 - 3^4) / (1 - 3)
S_4 = 2 × (1 - 81) / (-2)
S_4 = 2 × 40
S_4 = 80

So, the sum of the first four terms is 80.