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.