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The image you uploaded shows a worksheet that appears to ask for finding the sum of the series for each sequence provided. The sequences given are:

1. \( 2, 4, 6, 8, 10, \ldots \)
2. \( 2, 4, 8, 16, 32, \ldots \)
3. \( 3, 6, 9, 12, 15, \ldots \)
4. \( 1, 2, 4, 8, 16, \ldots \)
5. \( 5, 6, 7, 8, 9, \ldots \)

To solve this, you need to identify whether each sequence is arithmetic or geometric, then calculate the sum accordingly.

### Let's break down each sequence:

1. **Sequence 1**: \( 2, 4, 6, 8, 10, \ldots \)
   - **Type**: Arithmetic (common difference \( d = 2 \))
   - **Sum**: \( S_n = \frac{n}{2} \times (2a + (n-1)d) \)

2. **Sequence 2**: \( 2, 4, 8, 16, 32, \ldots \)
   - **Type**: Geometric (common ratio \( r = 2 \))
   - **Sum**: \( S_n = a \times \frac{1 - r^n}{1 - r} \) for \( r > 1 \)

3. **Sequence 3**: \( 3, 6, 9, 12, 15, \ldots \)
   - **Type**: Arithmetic (common difference \( d = 3 \))
   - **Sum**: \( S_n = \frac{n}{2} \times (2a + (n-1)d) \)

4. **Sequence 4**: \( 1, 2, 4, 8, 16, \ldots \)
   - **Type**: Geometric (common ratio \( r = 2 \))
   - **Sum**: \( S_n = a \times \frac{1 - r^n}{1 - r} \) for \( r > 1 \)

5. **Sequence 5**: \( 5, 6, 7, 8, 9, \ldots \)
   - **Type**: Arithmetic (common difference \( d = 1 \))
   - **Sum**: \( S_n = \frac{n}{2} \times (2a + (n-1)d) \)

Would you like the sums for a specific number of terms in each series, or do you have another request?

### Follow-up Questions:
1. How do you determine whether a sequence is arithmetic or geometric?
2. What is the formula for the sum of an infinite geometric series?
3. How does the common ratio affect the sum of a geometric series?
4. Can you explain the difference between an arithmetic series and an arithmetic sequence?
5. What happens to the sum of a geometric series when the common ratio is less than 1?

### Tip:
Remember, identifying the pattern in a sequence (arithmetic or geometric) is crucial for determining the correct formula to use for finding the sum.

Learn how to find the sum of arithmetic and geometric series with detailed explanations and examples. This problem involves identifying sequence types, applying relevant summation formulas, and understanding series properties. Suitable for students in Grades 9-12.

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