Arithmetic sequence
Definition
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference.
5 Must Know Facts For Your Next Test
- The general form of an arithmetic sequence is a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.
- The sum of the first n terms of an arithmetic sequence can be calculated using S_n = n/2 * (a_1 + a_n), where S_n is the sum, n is the number of terms, and a_n is the nth term.
- If you know any three of these four elements—first term, common difference, number of terms, or last term—you can find the fourth using arithmetic sequence formulas.
- Arithmetic sequences are linear because they increase or decrease by a fixed amount each time.
- In problems involving real-life contexts such as savings plans or installment payments, arithmetic sequences often model consistent changes over time.
Review Questions
- What formula would you use to find the nth term in an arithmetic sequence?
- How do you calculate the sum of the first n terms in an arithmetic sequence?
- What makes an arithmetic sequence different from other types of sequences?
"Arithmetic sequence" appears in:
Related terms
Geometric Sequence: A sequence where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio.
Common Difference: The fixed amount added to each term in an arithmetic sequence to get to the next term.
Series: The sum of all terms in a sequence.
