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The graph provided represents a geometric sequence \( g_n \) plotted against \( n \). In a geometric sequence, the ratio between successive terms is constant, leading to exponential growth or decay, depending on whether the common ratio is greater or less than 1.

### Analyzing the Options:
1. **The graph of the sequence is concave down** (selected option):
   - This is the correct description. The graph shows a downward curve, which is characteristic of exponential decay in geometric sequences with a ratio less than 1. The points on the graph decrease rapidly at first, then more slowly, forming a concave downward shape.

2. **The graph of the sequence shows a constant rate of change**:
   - This would describe an arithmetic sequence, not a geometric sequence. A geometric sequence has a multiplicative relationship between terms, so the rate of change is not constant.

3. **The sequence is decreasing and the average rate of change is decreasing**:
   - This would imply that the rate of decrease is slowing down more and more, which isn't the best description here. The average rate of change is actually increasing, as the values drop rapidly at first and then slow down.

4. **The sequence is decreasing and the average rate of change is increasing**:
   - This is close but not quite the best description. While the sequence does decrease and the rate of change seems to increase initially, the concave down description fits better because the curve shows a decelerating rate of decay.

Thus, **"The graph of the sequence is concave down"** is the most accurate description.

Would you like a further breakdown of the geometric sequence or more details on the reasoning? 

Here are some related questions for deeper understanding:

1. What is the general formula for a geometric sequence?
2. How can we determine the common ratio from a graph like this?
3. How does the shape of a graph change if the geometric sequence has a common ratio greater than 1?
4. What are some real-world applications of geometric sequences?
5. How would an arithmetic sequence differ visually from a geometric one?

**Tip:** When dealing with geometric sequences, always check whether the sequence is increasing or decreasing by looking at the common ratio \( r \). If \( |r| < 1 \), the sequence decays; if \( |r| > 1 \), it grows exponentially.

The figure above shows the graph of values of the geometric sequence, gn. Which of these best describes the sequence?

Analyze a geometric sequence graph to determine the shape and properties of the sequence. Learn how the common ratio affects the concave down nature of the graph in exponential decay sequences, ideal for high school students in Grades 9-12.

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