Arithmetic series

Definition

An arithmetic series is the sum of the terms in an arithmetic sequence, where each term after the first is obtained by adding a constant difference to the previous term.

5 Must Know Facts For Your Next Test

1. The general form of an arithmetic series is $S_n = a + (a+d) + (a+2d) + ... + [a+(n-1)d]$.
2. The sum of the first $n$ terms of an arithmetic series can be found using the formula $S_n = \frac{n}{2} (2a + (n-1)d)$ or $S_n = \frac{n}{2} (a + l)$, where $l$ is the last term.
3. In an arithmetic series, each term increases or decreases by a constant value known as the common difference ($d$).
4. If you know either two consecutive terms or one term and the common difference, you can find any other term in the series.
5. Arithmetic series are often used in real-world applications such as calculating total payments over time or summing evenly spaced data points.

Review Questions

• How do you find the sum of the first $n$ terms in an arithmetic series?
• What is the common difference in an arithmetic sequence and how does it affect the series?
• Given an initial term and common difference, how can you determine any specific term in an arithmetic series?

Related terms

Arithmetic Sequence: A sequence of numbers in which each term after the first is obtained by adding a fixed, non-zero number to the previous term.

Geometric Series: A series with a constant ratio between successive terms.

Common Difference: The fixed amount added to each term of an arithmetic sequence to get to the next term.