https://file.aiquickdraw.com/mathbot/file/17260578629714pecomsr.jpg

The image contains three geometric sequences and asks to determine the common ratio and find the sum of the terms for each sequence. Here's a breakdown of the problems:

1. **Sequence 1:**
   - Terms: 4, 12, 36, 108, ...
   - Find the sum up to 7 terms.

2. **Sequence 2:**
   - Terms: 2, 6, 18, 54, 162, ...
   - Find the sum up to 7 terms.

3. **Sequence 3:**
   - Terms: 7, 14, 28, 56, ...
   - Find the sum up to 8 terms.

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

Let’s calculate each one.

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Would you like me to proceed with the detailed calculations for each sequence?

Determine the common ratio and find the sum of the following geometric sequences:
1. 4, 12, 36, 108, ... up to 7 terms
2. 2, 6, 18, 54, 162, ... up to 7 terms
3. 7, 14, 28, 56, ... up to 8 terms

Learn how to find the common ratio and calculate the sum of geometric sequences. This problem involves series such as 4, 12, 36, 108,... and others. Step-by-step solutions provided. Suitable for Grades 9-12.

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