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The image contains a mathematical question in French related to a sequence \( v_n \), defined by \( v_n = 8n - 3 \), where \( n \) is a natural number. There are three sub-questions to be answered.

Let's break it down:

### Sequence Formula:
The sequence \( v_n \) is defined by \( v_n = 8n - 3 \).

#### Question 1: **Le premier terme de la suite est :**
You are asked to find the first term of the sequence. To find this, substitute \( n = 1 \) into the formula:
\[
v_1 = 8(1) - 3 = 8 - 3 = 5.
\]
So, the first term is 5, corresponding to **option c**.

#### Question 2: **Le deuxième terme de la suite est :**
You are asked to find the second term. Substitute \( n = 2 \):
\[
v_2 = 8(2) - 3 = 16 - 3 = 13.
\]
Thus, the second term is 13, corresponding to **option a**.

#### Question 3: **L'expression de \( v_{n+1} \) en fonction de \( n \) est :**
To express \( v_{n+1} \) in terms of \( n \), substitute \( n+1 \) into the formula:
\[
v_{n+1} = 8(n+1) - 3 = 8n + 8 - 3 = 8n + 5.
\]
So, the expression is \( 8n + 5 \), which corresponds to **option b**.

### Summary of Correct Answers:
1. **Le premier terme**: \( v_1 = 5 \) → **option c**.
2. **Le deuxième terme**: \( v_2 = 13 \) → **option a**.
3. **L'expression de \( v_{n+1} \)**: \( v_{n+1} = 8n + 5 \) → **option b**.

Would you like more details or have any questions about this?

Here are 5 related questions to expand your understanding:
1. How can you derive a general formula for the \( n \)-th term of a linear sequence?
2. What would be the 5th term of the sequence \( v_n = 8n - 3 \)?
3. How can you determine whether a sequence is arithmetic or geometric?
4. What is the common difference in the sequence \( v_n = 8n - 3 \)?
5. How do you express the general term \( v_n \) when given a recursive definition?

**Tip**: Always substitute values carefully in sequence formulas to avoid errors when calculating specific terms.

Soit la suite \( v_n \) une suite définie pour tout n entier naturel par \( v_n = 8n - 3 \). Indiquer dans chaque cas la bonne réponse.

Learn how to analyze an arithmetic sequence defined by v_n = 8n - 3, including finding the first and second terms, and expressing v_{n+1} in terms of n. This problem covers key sequence concepts and is suitable for students in Grades 9-12.

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