The common difference of the arithmetic series 5, 11, 17, 23, 29 is 6.
Understanding Arithmetic Series and Common Difference
An arithmetic series (or arithmetic sequence) is a sequence of numbers such that the difference between any two consecutive terms is constant. This constant difference is called the common difference.
The provided reference states: "This is an arithmetic sequence since there is a common difference between each term. In this case, adding 6 to the previous term in the sequence gives the next term."
Calculating the Common Difference
To find the common difference, subtract any term from its subsequent term. Here are a few calculations based on the given series:
- 11 - 5 = 6
- 17 - 11 = 6
- 23 - 17 = 6
- 29 - 23 = 6
As demonstrated, the difference between each pair of consecutive terms is consistently 6.
Summary Table
| Term | Value | Difference from Previous Term |
|---|---|---|
| 1st | 5 | - |
| 2nd | 11 | 6 |
| 3rd | 17 | 6 |
| 4th | 23 | 6 |
| 5th | 29 | 6 |
