Jaclyn, an investor, begins a start-up to revitalize homes in South Bend, Indiana. She begins with \(\$ 10,000\), making her investor 1. Each investor that joins will invest \(\$ 500\) more than the previous investor. How much does the 50th investor invest in the project? With that 50th investor, what is the total amount invested in the project?

Apply your knowledge of arithmetic sequences to these real-world scenarios.