The given sequence $1, 3, 9, 27, \ldots$ is a geometric series where the first term $a = 1$ and the common ratio $r = 3$.

The formula for the sum of the first $n$ terms of a geometric series is:

$S_n = a \frac{r^n - 1}{r - 1}$

Given that $n = 7$, let's calculate the sum:

$S_7 = 1 \cdot \frac{3^7 - 1}{3 - 1}$

Calculating $3^7$:

$3^7 = 2187$

Now, plug this into the formula:

$S_7 = \frac{2187 - 1}{2} = \frac{2186}{2} = 1093$

Therefore, the correct answer is:

A) 1093

Would you like more details or have any questions? Here are some related questions:

1. How do you identify a geometric series?
2. What is the general formula for any term in a geometric sequence?
3. How do you find the common ratio in a geometric series?
4. How does the sum formula change if the common ratio is negative?
5. How would the sum formula change for an infinite geometric series?

Tip: For a geometric series, always identify the first term and the common ratio before using the sum formula.