The following GMAT Problem Solving question tests your understanding of how to find the sum of an arithmetic sequence and also about observing patterns.

**Question 1**: If the sum of the first $100$ positive even integers is $10,100$, then what is the sum of the first $200$ positive even integers?

- $\quad 20,100$
- $\quad 20,200$
- $\quad 25,100$
- $\quad 40,100$
- $\quad 40,200$