No, the common difference of an arithmetic sequence is not obtained by adding the first term to the second term. Instead, it's found by subtracting a term from its immediate successor.
Here's a breakdown:
The common difference, usually denoted by 'd', is the constant amount added to each term in an arithmetic sequence to get the next term. The reference states that the formula to find the common difference, d, is:
d = a(n) - a(n - 1)
Where:
- a(n) = any term (nth term) in the sequence
- a(n - 1) = the term before a(n)
In simpler terms, to find the common difference, you subtract any term from the term that comes after it. You're finding the difference between consecutive terms, hence the name "common difference".
Example:
Consider the arithmetic sequence: 2, 5, 8, 11, 14...
To find the common difference:
- Take any two consecutive terms, for instance, 5 and 2.
- Subtract the first term from the second term: 5 - 2 = 3. So, d = 3.
- We can verify this with other consecutive terms. 8-5 = 3, 11-8 = 3, and so on.
Adding the first term to the second term (2 + 5 = 7) doesn't give you the common difference. Subtraction is key to find the common difference.
