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The problem asks to find the sum \( S_{15} \) for the arithmetic series given by:

\[ 5 + 9 + 13 + 17 + \dots \]

This is an arithmetic series where:
- The first term \( a_1 = 5 \)
- The common difference \( d = 4 \) (since \( 9 - 5 = 4 \))

The sum of the first \( n \) terms of an arithmetic series is given by the formula:

\[
S_n = \frac{n}{2} \times \left(2a_1 + (n-1) \times d\right)
\]

Here, we are asked to find \( S_{15} \), so \( n = 15 \). Plugging in the values:

\[
S_{15} = \frac{15}{2} \times \left(2 \times 5 + (15-1) \times 4\right)
\]

\[
S_{15} = \frac{15}{2} \times \left(10 + 14 \times 4\right)
\]

\[
S_{15} = \frac{15}{2} \times \left(10 + 56\right)
\]

\[
S_{15} = \frac{15}{2} \times 66
\]

\[
S_{15} = \frac{990}{2} = 495
\]

So, the sum \( S_{15} \) is 495.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do you derive the sum formula for an arithmetic series?
2. What happens if the common difference \( d \) is negative in an arithmetic series?
3. Can you determine the 15th term \( a_{15} \) of this series?
4. How does the formula for the sum of a series change if we only know the first and last terms?
5. What is the sum \( S_n \) of the series if \( n = 20 \)?

**Tip:** Always verify the common difference \( d \) in arithmetic series problems to avoid errors in calculation.

Discover how to find the sum S15 for the arithmetic series 5 + 9 + 13 + 17 + ... using the sum formula for an arithmetic sequence. Suitable for students in Grades 9-11.

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