The given series starts with \(17\), and the next term is \(34\), then \(57\), and so on until \(5126\). This suggests that the series is arithmetic, where the difference between consecutive terms is constant.

### Steps to represent this in sigma notation:

1. **Identify the first term (\(a\)):**
   The first term \(a = 17\).

2. **Find the common difference (\(d\)):**
   The second term is \(34\), and the first term is \(17\), so the common difference is:
   \[
   d = 34 - 17 = 17.
   \]
   
3. **Find the number of terms (\(n\)):**
   The general form for the \(n\)-th term of an arithmetic sequence is:
   \[
   a_n = a + (n-1) \cdot d.
   \]
   The last term is \(5126\), so:
   \[
   5126 = 17 + (n-1) \cdot 17.
   \]
   Simplifying this equation:
   \[
   5126 - 17 = (n-1) \cdot 17,
   \]
   \[
   5109 = (n-1) \cdot 17,
   \]
   \[
   n-1 = \frac{5109}{17} = 300,
   \]
   \[
   n = 301.
   \]
   So, there are \(301\) terms.

4. **Write the sigma notation:**
   The arithmetic series can be expressed in sigma notation as:
   \[
   \sum_{k=1}^{301} \left( 17k \right).
   \]

Thus, the sigma notation for the series is:
\[
\sum_{k=1}^{301} \left( 17k \right).
\]

Would you like any further explanation or details on this?

### Related Questions:
1. How do you calculate the sum of an arithmetic series using sigma notation?
2. What is the formula for the sum of the first \(n\) terms in an arithmetic series?
3. Can this series be expressed in a different way using sequences?
4. How do you derive the general formula for the \(n\)-th term in an arithmetic series?
5. What are some common applications of sigma notation in calculus?

**Tip:** The sum of an arithmetic series can be calculated using the formula \( S_n = \frac{n}{2} \cdot (a + l) \), where \(a\) is the first term, \(l\) is the last term, and \(n\) is the number of terms.

Learn how to express the arithmetic series 17 + 34 + 57 + … + 5126 in sigma notation. This solution includes identifying the first term, common difference, number of terms, and the final sigma notation. Suitable for Grades 9-12.

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