Common difference

The common difference is the constant value by which each term in an arithmetic sequence increases or decreases. It is the difference between any two consecutive terms in the sequence. For example, in the sequence 2, 5, 8, 11, 14, the common difference is 3 because each term increases by 3.

Definition:

The common difference of an arithmetic sequence is the constant difference between consecutive terms in the sequence.

Formula:

The common difference, d, between consecutive terms a_n and a_{n+1} is given by:

```
d = a_{n+1} - a_n
```

Properties:

- All terms in an arithmetic sequence have the same common difference.
- The common difference determines the slope of the line that represents the sequence when plotted on a graph.
- The common difference can be positive, negative, or zero.

Finding the Common Difference:

To find the common difference of an arithmetic sequence, subtract the first term from the second term, the second term from the third term, and so on. If the same difference is obtained each time, then it is the common difference.

Example:

Given the arithmetic sequence 2, 5, 8, 11, ..., find the common difference.

```
d = 5 - 2 = 3
d = 8 - 5 = 3
d = 11 - 8 = 3
```

Therefore, the common difference of the sequence is 3.

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