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The problem asks to calculate the sum of the first 197 terms of the arithmetic progression:

\[ 112, 131, 150, 169, 188, \ldots \]

This is an arithmetic progression (AP), where the first term \(a_1 = 112\) and the common difference \(d = 131 - 112 = 19\).

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

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

where:
- \(n = 197\) (the number of terms),
- \(a_1 = 112\) (the first term),
- \(d = 19\) (the common difference).

Let's calculate the sum.

The sum of the first 197 terms of the arithmetic progression is \( 388,878 \), which corresponds to option **d. 388878**.

Would you like more details or have any questions about the solution?

Here are five related questions to deepen your understanding:
1. How can the sum formula for arithmetic progression be derived?
2. What would happen if the common difference in this sequence were negative?
3. How can you find the \(n\)-th term in an arithmetic progression?
4. What is the relationship between the sum of terms and the number of terms in an arithmetic progression?
5. How would the solution change if only 100 terms were summed?

**Tip:** For any arithmetic progression, knowing the first term and the common difference helps you easily determine the sum or any specific term.

Calcular la suma de los primeros 197 términos de la siguiente progresión: 112, 131, 150, 169, 188, ...

Learn how to calculate the sum of the first 197 terms of the arithmetic progression starting with 112, 131, 150, 169, 188. This problem involves the sum formula for an arithmetic progression and the application of sequences concepts. Suitable for students in Grades 9-12.

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