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The question shown in the image involves a point-based system where each player earns points for drawing green cards. Here’s the breakdown:

- The first green card gives **1 point**.
- The second green card gives **3 points**.
- The third green card gives **5 points**, and so on.
- Essentially, each new green card gives **2 points more** than the previous card.

The total points a player with **n** green cards would get is the sum of the first **n** odd numbers. The sum of the first **n** odd numbers is known to be:

\[
S = n^2
\]

Thus, the total points obtained for **n** green cards is \( n^2 \).

So, the correct answer is **D. n²**.

Would you like more details or have any other questions?

### Related Questions:
1. How do we derive the sum of the first n odd numbers?
2. What if the points increased by a different factor, say 3 instead of 2?
3. How can this system be generalized to other patterns of points?
4. What are other mathematical series similar to this point system?
5. How can you represent this sequence graphically?

### Tip:
The sum of the first **n** odd numbers is always a perfect square, which is a useful property in many mathematical problems.

In a board game, every time a player gets a green card, they earn points. The first green card earns 1 point, the second earns 3 points, the third earns 5 points, and so on, with each green card earning 2 more points than the previous one. What is the total number of points for a player with n green cards?

Explore how to calculate the total points for n green cards in a board game where each new card earns 2 more points than the previous one. Learn about the formula for the sum of the first n odd numbers and its applications. Perfect for students in Grades 6-8.

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