Arithmetic Sequence Rule
An arithmetic sequence is a list of numbers where the difference between consecutive terms stays constant. This constant difference is often called the common difference.
Method
- Identify the pattern: Compare two neighboring terms to find how much the sequence changes each time.
- Find the rule: Write the term you need in a form that adds the same change step by step. For an arithmetic sequence, each new term is obtained by adding the common difference to the previous term.
- Use the given information carefully: If you are given an initial term and the change, apply the pattern consistently until you reach the required term.
- Simplify the final answer: Combine any like terms or reduce the expression as needed.
Check your work
- Substitute your result back into the pattern to see whether the differences between terms remain constant.
- Make sure each step changes by the same amount.
- If the answer is an expression, verify that it matches the sequence rule and is fully simplified.
Tip
A correct arithmetic-sequence rule should produce terms with a repeated, unchanging difference. If the differences are not equal, recheck the arithmetic in your steps.