No, a common difference of an arithmetic series cannot be found by subtracting any term from the previous term.
The common difference in an arithmetic sequence is found by subtracting any term from the following term. As stated in the reference, "the common difference in an arithmetic sequence can be found by choosing any term and subtracting the previous term from it. Written algebraically, this says d = an+1 − an where an+1 is some term in the sequence and an is the previous term." This means you must subtract the term that comes before the term you chose, not the other way around. If you were to subtract a term from the previous term, you would get the negative of the common difference.
For example:
- In the arithmetic sequence 2, 5, 8, 11, 14... the common difference is 3.
- If we choose 5 (an), then the following term is 8 (an+1).
- So the common difference is d = 8 - 5 = 3.
- If we subtract 5 from 2, we get -3.
- In the sequence 10, 7, 4, 1, -2.... the common difference is -3.
- If we choose 7(an), then the following term is 4 (an+1).
- So the common difference is d = 4 - 7 = -3.
- If we subtract 7 from 10, we get 3.
Therefore, to find the common difference, always subtract a term from the term that follows it.
| Term | Following Term | Correct Subtraction (to find common difference) | Incorrect Subtraction |
|---|---|---|---|
| an | an+1 | an+1 - an | an - an+1 |
