The common difference of the arithmetic sequence 5, 9, 13 is 4.
Understanding Arithmetic Sequences
An arithmetic sequence is a series of numbers where the difference between any two consecutive terms is constant. This constant difference is known as the common difference. To find the common difference in an arithmetic sequence, you simply subtract any term from the term that follows it.
Calculating the Common Difference
- Sequence: 5, 9, 13, ...
- First Term (a₁): 5
- Second Term (a₂): 9
- Third Term (a₃): 13
To find the common difference (d), we can use the following calculation:
- d = a₂ - a₁ = 9 - 5 = 4
- Also, d = a₃ - a₂ = 13 - 9 = 4
As we can see, the common difference between consecutive terms is consistently 4.
Example from the Reference
The provided reference states: "Hence, we have found the common difference of the arithmetic sequence 5, 9, 13, 17,.... The common difference is 4." This confirms our calculation.
Therefore, the common difference for the arithmetic sequence 5, 9, 13 is indeed 4.
