The common difference of an arithmetic sequence can be found by subtracting any term from its subsequent term. The formula formalizes this process.
Understanding Arithmetic Sequences and Common Difference
An arithmetic sequence is a series of numbers where the difference between any two successive members is a constant. This constant difference is known as the "common difference".
The Formula for Common Difference
According to the reference, the formula to find the common difference (d) of an arithmetic sequence is:
d = a(n) - a(n - 1)
Where:
- d is the common difference.
- a(n) is any term in the sequence.
- a(n - 1) is the term that immediately precedes a(n) in the sequence.
In simpler terms, you subtract any term from the term that comes after it.
Steps to find the common difference:
- Identify two consecutive terms: Choose any two terms in the sequence that are next to each other.
- Subtract: Subtract the first term (a(n-1)) from the second term (a(n)). The result is the common difference.
Example
Let's say you have the arithmetic sequence: 2, 5, 8, 11, 14...
To find the common difference:
- Choose two consecutive terms: Let's choose 5 and 2. Here, a(n) = 5 and a(n-1) = 2.
- Apply the formula: d = 5 - 2 = 3.
Therefore, the common difference of this arithmetic sequence is 3. You could verify this by using another pair of consecutive terms such as 8 and 5: d = 8 - 5 = 3.
