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The question is in Catalan, and it translates to:

> "Find the sum of the first 50 terms of the following arithmetic progression."
>
> \( a_n = 7n - 4 \)

### Solution

1. **Identify the first term and common difference:**

   For an arithmetic sequence given by \( a_n = 7n - 4 \):
   - The first term, \( a_1 \), is found by setting \( n = 1 \):
     \[
     a_1 = 7(1) - 4 = 3
     \]
   - The common difference, \( d \), is calculated as the difference between the second term \( a_2 \) and the first term \( a_1 \):
     \[
     a_2 = 7(2) - 4 = 10
     \]
     \[
     d = a_2 - a_1 = 10 - 3 = 7
     \]

2. **Use the sum formula for an arithmetic sequence:**

   The sum of the first \( n \) terms of an arithmetic sequence is given by:
   \[
   S_n = \frac{n}{2} (2a_1 + (n - 1)d)
   \]
   Here:
   - \( n = 50 \)
   - \( a_1 = 3 \)
   - \( d = 7 \)

   Substituting these values:
   \[
   S_{50} = \frac{50}{2} \left( 2 \times 3 + (50 - 1) \times 7 \right)
   \]
   Simplify inside the parentheses:
   \[
   S_{50} = 25 \left( 6 + 49 \times 7 \right)
   \]
   \[
   S_{50} = 25 \left( 6 + 343 \right)
   \]
   \[
   S_{50} = 25 \times 349 = 8725
   \]

### Answer:
The sum of the first 50 terms is \( S_{50} = 8725 \).

Would you like further clarification on any step?

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#### Related Questions:
1. How do you find the sum of an arithmetic sequence if only the first and last terms are known?
2. What would be the sum of the first 100 terms for the same sequence?
3. How can you find the 50th term directly from the formula \( a_n = 7n - 4 \)?
4. If the common difference changes, how does that affect the sum of the sequence?
5. Can this formula be used to find the sum of geometric sequences as well? Why or why not?

#### Tip:
When dealing with arithmetic sequences, knowing the first term and the common difference allows you to quickly find the sum of any number of terms.

Troba la suma dels 50 primers termes d'aquestes progressions aritmètiques.
a) a_n = 7n - 4

Learn how to find the sum of the first 50 terms in the arithmetic sequence defined by a_n = 7n - 4. This solution covers arithmetic sequences, calculating terms, and using the summation formula. Ideal for Grade 10 students.

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