a set of numbers where the difference is the same between any two consecutive terms
is called an arithmetic sequence or arithmetic progression. It has a common difference d, and the nth term can be found using the formula a_n = a_1 + (n-1)d, where a_1 is the first term. Examples of arithmetic sequences include:
1. 3, 7, 11, 15, 19, ... (common difference d = 4)
2. -5, -2, 1, 4, 7, ... (common difference d = 3)
3. 10, 10, 10, 10, 10, ... (common difference d = 0, a constant sequence)
Arithmetic sequences can also be represented by a sequence of dots or tick marks, where the distance between any two consecutive dots is the common difference. For example:
3 · · · 7 · · · 11 · · · 15 · · · 19 · · · ...
In this sequence, the common difference between any two consecutive dots is 4.