The common difference of the arithmetic sequence 5, 10, 15, 20 is 5.
Understanding Arithmetic Sequences
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. This constant difference is known as the "common difference".
Identifying the Common Difference
In the given sequence (5, 10, 15, 20), we can identify the common difference by subtracting any term from its succeeding term.
- 10 - 5 = 5
- 15 - 10 = 5
- 20 - 15 = 5
As demonstrated, the difference between each pair of consecutive terms is consistently 5. The reference states that "The pattern in the sequence 5, 10, 15, 20 is that each number increases by 5. This sequence is an example of an arithmetic sequence, where the difference between consecutive terms is constant. In this case, the common difference is 5."
Example Calculation
To further clarify, consider the general form of an arithmetic sequence:
a, a + d, a + 2d, a + 3d, ...
where:
- a = the first term
- d = the common difference
In our sequence, a = 5. Therefore, each subsequent term is obtained by adding 'd' (the common difference) to the previous term.
Summary
| Term | Value | Calculation |
|---|---|---|
| 1st | 5 | |
| 2nd | 10 | 5 + 5 |
| 3rd | 15 | 10 + 5 |
| 4th | 20 | 15 + 5 |
This table illustrates how each term is generated by adding the common difference (5) to the preceding term.
