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 general form of an arithmetic sequence can be written as $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.
2. The sum of the first $n$ terms of an arithmetic sequence (the arithmetic series) can be calculated using the formula $S_n = \frac{n}{2}(2a_1 + (n-1)d)$.
3. If you know any two consecutive terms in an arithmetic sequence, you can find the common difference by subtracting them: $d = a_{n+1} - a_n$.
4. In an arithmetic sequence, each term increases or decreases by a fixed amount called the common difference.
5. Arithmetic sequences are linear; plotting their terms on a graph results in points that lie on a straight line.

Review Questions

• What is the formula for finding the nth term of an arithmetic sequence?
• How do you calculate the sum of the first n terms in an arithmetic sequence?
• Given two consecutive terms in an arithmetic sequence, how do you find the common difference?

Related terms

Common Difference: The constant amount that each term in an arithmetic sequence increases or decreases by.

$a_1$: The first term in a sequence.

$S_n$: The sum of the first n terms of a sequence.