To accurately determine the common difference, an arithmetic sequence must be provided. Assuming the question intends to ask how to find the common difference of a given arithmetic sequence, this explanation and formula are for that purpose.
The common difference in an arithmetic sequence is the constant value added or subtracted to get from one term to the next. According to the provided reference, we can find the common difference (denoted as 'd') using the following formula:
d = a(n) - a(n - 1)
Where:
- a(n) is any term in the sequence.
- a(n-1) is the term that immediately precedes a(n).
How to Find the Common Difference
- Select any two consecutive terms from the sequence. For example, you can select the 2nd and 3rd terms, or the 5th and 6th terms.
- Subtract the first selected term (the one preceding the second term) from the second selected term. The result of this subtraction is the common difference 'd'.
Example:
Let's say the arithmetic sequence is: 2, 5, 8, 11, 14...
Using the formula, we can find the common difference:
-
Let's take a(2) = 5 and a(1) = 2
d = a(2) - a(1) = 5 - 2 = 3
-
Let's take a(4) = 11 and a(3) = 8
d = a(4) - a(3) = 11 - 8 = 3
In this example, the common difference is 3. This value will remain constant throughout the sequence.
Key Points to Remember
- The common difference can be positive, negative, or zero.
- If the common difference is positive, the sequence is increasing.
- If the common difference is negative, the sequence is decreasing.
- If the common difference is zero, the sequence is constant.
