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.
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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.
The sum of the first $n$ terms of an arithmetic sequence (the arithmetic series) can be calculated using the formula $S_n = \frac{n}{2}(2a_1 + (n-1)d)$.
If you know any two consecutive terms in an arithmetic sequence, you can find the common difference by subtracting them: $d = a_{n+1} - a_n$.
In an arithmetic sequence, each term increases or decreases by a fixed amount called the common difference.
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.