Question

An Incomplete table of sequences and common ratios is shown.(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Complete the table.

Sequence Common Ratio
3,6,12,24,48,.... Response area
15,9,275
,8125
,243125
,... Response area

Answer 1

To complete the table, let’s first examine the sequences provided.

1. **First Sequence: 3, 6, 12, 24, 48,...**
- To find the common ratio, divide any term by its preceding term.
- 6 / 3 = 2
- 12 / 6 = 2
- 24 / 12 = 2
- 48 / 24 = 2
- The common ratio for this sequence is **2**.

2. **Second Sequence: 15, 9, 275,...**
- This sequence appears to be different as it does not follow a standard geometric progression based on the initial terms provided.
- However, taking a closer look at the values, we can check if the numbers indicate a geometric sequence or another specific pattern with the provided options (8125, 243125).

3. **Third Sequence: After analyzing the response area (15, 9, 275), let's calculate whether the subsequent numbers fit as the next terms.**
- 15 to 9 indicates a decrease, suggesting a negative ratio or different sequence.
- Continuing, we will see if there's a common ratio from 9 to 275 and whether the next numbers would follow logically from 8125 and 243125.
- Hence we will analyze the ratio.

For a potential ratio that leads to a ""geometric sequence," you would need to check for multiplicative patterns.

However, considering the provided responses for adjustment, we can use:
- **1st Sequence**: Common Ratio = 2.
- **2nd Sequence**: If a specific multiplication leads logically to the options, choosing based on what fits can lead us to options:
- Final adjustments based on trial could be collecting the sequences to fit.

Final completion:
- **Common ratio for the first sequence**: 2
- For the second sequence:
- If it follows a pattern of \(r\): This sequence could aim at another structure where an option finalizes into trends.

Table completion:
```
| Sequence | Common Ratio |
|----------------------|--------------|
| 3,6,12,24,48,... | 2 |
| 15,9,275,... | 8125 |
```

Final Answer:
- For the first sequence: **Common Ratio: 2**
- For the second sequence: **Next term: 8125**

Note: The calculation needs to logically fit each from the options provided unless a specific geometric approach leads 275 towards a simplistically accurate outcome.