Easy Ways to Understand Sequences and Series

1. Types of Sequences:

• Arithmetic Sequences are made by adding the same number each time. We call this number $d$. The formula looks like this: $a_n = a_1 + (n-1)d$. In this formula, $a_n$ is the term number we want to find.
• Geometric Sequences are different because we multiply by a constant number called $r$. The formula for this is $a_n = a_1 \cdot r^{(n-1)}$. Here, $a_n$ is also the term number.

2. Seeing the Difference:

• Use graphs to see how arithmetic sequences grow in a straight line, while geometric sequences grow much faster in a curve.
• This makes it easier to notice how quickly each type of sequence changes.

3. Practice Problems:

• Try solving problems with both types of sequences regularly. For example, find the 10th term of this arithmetic sequence: $a_n = 5 + (n-1)3$. And for geometric, use this: $a_n = 2 \cdot 3^{(n-1)}$.
• Start easy and then make the problems a bit harder as you go. This helps you get more confident!

4. Real-Life Examples:

• Connect the idea of sequences to everyday life. For example, think of arithmetic sequences when budgeting money, and geometric sequences when looking at how populations grow.

5. Team Learning:

• Working with others can help you learn better. Studies show that students who study in groups can do up to 25% better than those who study alone. So, don’t be afraid to ask your friends for help!