The common difference of an arithmetic sequence is the constant value added to each term to get the next term in the sequence.
To elaborate:
- It's the value you consistently add (or subtract) to move from one term to the next.
- It's denoted by the variable d.
- You can find d by subtracting any term from the term that immediately follows it.
Mathematically:
If you have an arithmetic sequence: a1, a2, a3, a4,... then the common difference, d, is calculated as:
d = a2 - a1 = a3 - a2 = a4 - a3, and so on. In general:
d = an - an-1
Example:
Consider the arithmetic sequence: 2, 5, 8, 11, 14,...
To find the common difference:
- d = 5 - 2 = 3
- d = 8 - 5 = 3
- d = 11 - 8 = 3
- d = 14 - 11 = 3
Therefore, the common difference, d, in this example is 3.
