Term

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

1. The formula for the nth term of an arithmetic sequence is given by a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.
2. The sum of the first n terms of an arithmetic sequence can be found using S_n = n/2 * (2a_1 + (n-1)d).
3. The common difference can be positive, negative, or zero.
4. In an arithmetic sequence, if you know any three of these four elements—first term, number of terms, common difference, and last term—you can find the fourth.
5. Arithmetic sequences are used in various real-world contexts such as calculating loan payments and analyzing patterns in data sets.

Review Questions

• What is the common difference in the arithmetic sequence 3, 7, 11, 15?
• How do you find the nth term of an arithmetic sequence?
• Calculate the sum of the first 10 terms in an arithmetic sequence with a first term of 5 and a common difference of 3.

Related terms

Geometric Sequence: A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Common Difference: The constant difference between consecutive terms in an arithmetic sequence.

Series: The sum of the terms in a sequence.