The common difference in the arithmetic sequence 2, 8, 14, 20 is 6.
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.
Calculating the Common Difference
To find the common difference in an arithmetic sequence, you simply subtract any term from the term that follows it. Let's apply this to the given sequence 2, 8, 14, 20:
- Step 1: Subtract the first term from the second term: 8 - 2 = 6
- Step 2: Subtract the second term from the third term: 14 - 8 = 6
- Step 3: Subtract the third term from the fourth term: 20 - 14 = 6
Since the difference is consistently 6, the common difference of the sequence is indeed 6.
Example
As stated in the reference, the arithmetic sequence 2, 8, 14, 20, 26,... has a common difference of 6. This demonstrates that with a consistent difference (in this case 6), each succeeding term can be obtained by adding 6 to the previous term.
Key Points
- The common difference is constant throughout the arithmetic sequence.
- You can find the common difference by subtracting any term from the term directly following it.
