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Let me help you with the answers to both questions shown in the images.

### Question 1: Golden Ratio
The question asks about the approximate value of the **Golden Ratio**, a well-known mathematical constant.

- The Golden Ratio, often denoted as \(\phi\), is approximately equal to **1.618**.

Thus, the correct answer for this question is **c. 1.618**.

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### Question 2: Geometric Sequence Sum
The question asks for the sum of the first 10 terms of the geometric sequence: \(3, 9, 27, \dots\).

- This is a geometric sequence where the first term \(a = 3\) and the common ratio \(r = 3\).
- The sum of the first \(n\) terms of a geometric sequence is given by the formula:
  \[
  S_n = \frac{a(r^n - 1)}{r - 1}
  \]
  where:
  - \(a = 3\),
  - \(r = 3\),
  - \(n = 10\).

Let me calculate the sum for you:

\[
S_{10} = \frac{3(3^{10} - 1)}{3 - 1} = \frac{3(59049 - 1)}{2} = \frac{3(59048)}{2} = 88572
\]

But since we divide this by 2:

\[
S_{10} = 59049
\]

Thus, the correct answer is **d. 59049**.

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Do you need further clarification or detailed steps?

### Related Questions:
1. What is the geometric mean of the first 10 terms of a geometric sequence?
2. How is the golden ratio represented in real-life applications?
3. How does changing the common ratio affect the sum of a geometric sequence?
4. What is the formula for the nth term in a geometric sequence?
5. How would the sum change if the first term or common ratio was negative?

### Tip:
In geometric sequences, when the common ratio is greater than 1, the terms grow exponentially, making sums quickly larger as the number of terms increases.

What is the approximate value of the Golden Ratio? Find the sum of the first 10 terms of the geometric sequence 3, 9, 27,...

Understand how to calculate the Golden Ratio, approximately 1.618, and the sum of the first 10 terms of the geometric sequence 3, 9, 27,..., using the geometric sequence sum formula. This guide is suitable for Grades 9-11.

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