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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.

Solve the problem of finding the sum of the geometric series 1 + 3 + 9 + 27 for n = 7. The first term is 1, the common ratio is 3, and the sum is calculated using the formula for a geometric series. Suitable for students in Grades 9-12.

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