Let's create an arithmetic sequence:

Example sequence:
4, 8, 12, 16, 20, ...

1. Common Difference (d):

The common difference $d$ is the difference between any two consecutive terms.
For example, $d = 8 - 4 = 4$, and $d = 12 - 8 = 4$, so the common difference is $d = 4$.

2. Finding $a_6$:

The general formula for the $n$-th term of an arithmetic sequence is: $a_n = a_1 + (n - 1) \cdot d$ Where:

• $a_n$ is the $n$-th term
• $a_1$ is the first term
• $d$ is the common difference
• $n$ is the position of the term

To find $a_6$, we substitute the known values into the formula:

• $a_1 = 4$ (the first term)
• $d = 4$ (the common difference)
• $n = 6$

$a_6 = 4 + (6 - 1) \cdot 4$ $a_6 = 4 + 5 \cdot 4$ $a_6 = 4 + 20$ $a_6 = 24$

So, $a_6 = 24$.

Summary:

• Arithmetic Sequence: 4, 8, 12, 16, 20, ...
• Common Difference (d): 4
• $a_6$: 24

Would you like more details or have any questions on this?
Here are some related questions:

1. How do you find the $n$-th term of an arithmetic sequence?
2. What happens if the common difference is negative?
3. How can you find the sum of the first $n$ terms in an arithmetic sequence?
4. How do you recognize an arithmetic sequence in a real-world situation?
5. Can an arithmetic sequence have a common difference of zero?

Tip: In an arithmetic sequence, the common difference remains constant, making it easy to predict future terms.