Constant difference
Definition
Constant difference is the fixed amount that each term in an arithmetic sequence increases or decreases by. It is also known as the common difference and is denoted by 'd'.
5 Must Know Facts For Your Next Test
- The constant difference can be found by subtracting any term from the subsequent term in the sequence.
- In an arithmetic sequence, if you know the first term and the constant difference, you can find any term in the sequence using the formula: a_n = a_1 + (n-1)d.
- The constant difference can be positive, negative, or zero depending on whether the sequence is increasing, decreasing, or constant.
- If the constant difference is positive, each successive term is greater than the previous one; if it’s negative, each successive term is smaller.
- Arithmetic sequences with a non-zero constant difference are linear when plotted on a graph.
Review Questions
- How do you calculate the constant difference in an arithmetic sequence?
- What happens to an arithmetic sequence if its constant difference is negative?
- Can an arithmetic sequence have a constant difference of zero? What would this look like?
"Constant difference" appears in:
Related terms
arithmeticSequence: A sequence of numbers in which the difference between consecutive terms is constant.
commonDifference: Another name for the constant difference in an arithmetic sequence.
a_nFormula: The formula used to find any term in an arithmetic sequence: a_n = a_1 + (n-1)d.
