An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed number, called the common difference, to the previous term. This fixed number is also known as the arithmetic step or difference between terms.
For example, consider the following arithmetic sequence: 2, 5, 8, 11, 14, 17, …
In this sequence, the common difference is 3, because each term is obtained by adding 3 to the previous term.
An arithmetic sequence can be represented by the following general formula: a, a + d, a + 2d, a + 3d, …
In this formula, a is the first term in the sequence and d is the common difference.
For example, in the arithmetic sequence 2, 5, 8, 11, 14, 17, … the first term is 2 and the common difference is 3. Therefore, the general formula for this arithmetic sequence is: 2, 2 + 3, 2 + 2(3), 2 + 3(3), …
An arithmetic sequence is also known as an arithmetic progression.
Examples of arithmetic sequences:
1, 4, 7, 10, 13, 16, …
In this arithmetic sequence, the common difference is 3.
10, 7, 4, 1, -2, -5, …
In this arithmetic sequence, the common difference is -3.
-2, 1, 4, 7, 10, 13, …
In this arithmetic sequence, the common difference is 3.
100, 95, 90, 85, 80, 75, …
In this arithmetic sequence, the common difference is -5.
2, 6, 10, 14, 18, 22, …
In this arithmetic sequence, the common difference is 4.
Quiz:
- What is an arithmetic sequence?
- What is the general formula for an arithmetic sequence?
- What is the common difference in the arithmetic sequence 1, 4, 7, 10, 13, 16, …?
- What is the common difference in the arithmetic sequence 10, 7, 4, 1, -2, -5, …?
- What is the common difference in the arithmetic sequence -2, 1, 4, 7, 10, 13, …?
- What is the common difference in the arithmetic sequence 100, 95, 90, 85, 80, 75, …?
- What is the common difference in the arithmetic sequence 2, 6, 10, 14, 18, 22, …?
- What is the 5th term in the arithmetic sequence 1, 4, 7, 10, 13, 16, …?
- What is the 7th term in the arithmetic sequence 10, 7, 4, 1, -2, -5, …?
- What is the 6th term in the arithmetic sequence -2, 1, 4, 7, 10, 13, …?
