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The problem in the image asks to calculate the sum of an arithmetic sequence with the given terms:

\[
9 + 5 + 1 + \dots + (-571)
\]

We are told that the terms follow an arithmetic progression. In an arithmetic sequence, each term differs from the next by a constant difference, known as the common difference.

### Given:
- First term \( a_1 = 9 \)
- Common difference \( d = 5 - 9 = -4 \)
- Last term \( a_n = -571 \)

### Steps to solve:

1. **Find the number of terms \( n \):**
   The formula for the \( n \)-th term of an arithmetic sequence is:
   \[
   a_n = a_1 + (n - 1) \cdot d
   \]
   Substituting the known values:
   \[
   -571 = 9 + (n - 1) \cdot (-4)
   \]
   Solving for \( n \):
   \[
   -571 - 9 = (n - 1) \cdot (-4)
   \]
   \[
   -580 = (n - 1) \cdot (-4)
   \]
   \[
   n - 1 = \frac{-580}{-4} = 145
   \]
   \[
   n = 146
   \]
   So, there are 146 terms in the sequence.

2. **Calculate the sum \( S_n \):**
   The sum of the first \( n \) terms of an arithmetic sequence is given by the formula:
   \[
   S_n = \frac{n}{2} \cdot (a_1 + a_n)
   \]
   Substituting the values:
   \[
   S_{146} = \frac{146}{2} \cdot (9 + (-571))
   \]
   \[
   S_{146} = 73 \cdot (-562)
   \]
   \[
   S_{146} = -41026
   \]

Therefore, the sum of the arithmetic sequence is \( -41,026 \).

Would you like a detailed explanation of any step? 

Here are 5 related questions to deepen understanding:

1. How do you identify an arithmetic sequence?
2. Can the common difference in an arithmetic sequence be positive?
3. What happens if the first term or the last term is zero in the sum formula?
4. How can you find the common difference if it's not given directly?
5. Can we calculate the sum of an infinite arithmetic sequence?

**Tip:** In an arithmetic sequence, the sum depends heavily on the number of terms and the common difference. Make sure to check both carefully.

Calcular la siguiente suma: 9 + 5 + 1 + ... + (-571) asumiendo que los términos son consecutivos de una sucesión aritmética.

This problem involves calculating the sum of an arithmetic sequence starting from 9, with a common difference of -4, and ending at -571. Learn how to use the arithmetic sequence formula to find the number of terms and compute the series' total sum.

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