The common difference in an arithmetic sequence is the constant amount added or subtracted between each consecutive term.
Understanding Common Difference
A sequence is a list of numbers arranged in a specific order. An arithmetic sequence is a special type of sequence where each term after the first is obtained by adding a constant value to the preceding term. This constant value is what we call the common difference.
How to Find the Common Difference
According to the reference, to find the common difference, you can:
- Subtract the first term from the second term.
- Subtract the second term from the third term.
- And so on...
If the result is the same no matter which pair of consecutive terms you subtract, then you have found the common difference for an arithmetic sequence.
Example
Let’s consider a sequence: 2, 10, 18, 26...
- Subtract the first term from the second: 10 - 2 = 8
- Subtract the second term from the third: 18 - 10 = 8
- Subtract the third term from the fourth: 26 - 18 = 8
Since the result is consistently 8, the common difference in this sequence is 8. The reference example also shows an arithmetic sequence where each term adds 8, confirming a common difference of 8.
Key Takeaways
- The common difference is crucial for identifying an arithmetic sequence.
- It's always the same value added or subtracted to get the next term.
- You can find it by subtracting any term from its following term.
