When we explore sequences and series, we discover just how interesting they are in everyday life, even if we don’t notice them all the time.

So, what is a sequence? It's simply an ordered list of numbers. A series, on the other hand, is what you get when you add those numbers together. Here’s why they’re important in the world around us:

1. Finance and Economics

• Investments: When you put money into a bank account or stocks, its growth can often be explained by a geometric series. This means that as you earn interest on your savings, the total amount can be shown through a series.

• Loans: When you borrow money, the way you pay it back often forms an arithmetic series. This is where each payment you make is the same amount.

2. Architecture and Engineering

• Design: The Fibonacci sequence, which is a special type of sequence, is often found in designs. It helps create buildings and artwork that look really nice. The sizes and shapes in these designs sometimes depend on these specific numbers.

3. Computer Science

• Algorithms: In computer science, many processes (called algorithms) use sequences. For example, when sorting files or data, the steps taken can be examined through series to see how fast they work.

4. Natural Sciences

• Population Growth: Scientists often use sequences to study how populations grow. They can make predictions about future populations based on past information.

So, whether you’re figuring out your investment returns or observing patterns in nature, sequences and series are everywhere! It’s pretty awesome to see that what you learn in math class can be used in so many real-life situations.