A sequence whose consecutive terms have a common difference is called an arithmetic sequence (or arithmetic progression). In this sequence, the difference between any two consecutive terms remains constant, and this constant is known as the common difference.

The general form of an arithmetic sequence is:

$a_n = a_1 + (n-1) \cdot d$

Where:

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

Example:

If the first term is 2 and the common difference is 3, the sequence will be:

$2, 5, 8, 11, 14, \dots$

Each term increases by 3, which is the common difference.

Would you like more details or have any questions?

Here are five related questions for further exploration:

1. How do you find the sum of the first $n$ terms of an arithmetic sequence?
2. How can you find the common difference if two terms of the sequence are given?
3. What is the formula for the $n$-th term of an arithmetic sequence?
4. Can an arithmetic sequence have a negative common difference?
5. How do arithmetic sequences apply to real-world problems?

Tip: The sum of an arithmetic sequence is called an arithmetic series and has a specific formula for calculation.