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

1. The general form of an arithmetic sequence is $a_n = a_1 + (n-1)d$, 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 (arithmetic series) can be calculated using $S_n = \frac{n}{2} \times (2a_1 + (n-1)d)$ or $S_n = \frac{n}{2} \times (a_1 + a_n)$.
3. In any arithmetic sequence, the nth term can be found if you know any three of these values: first term ($a_1$), common difference ($d$), number of terms ($n$), and nth term ($a_n$).
4. Arithmetic sequences can be either increasing (if $d > 0$) or decreasing (if $d < 0$).
5. If all terms in an arithmetic sequence are added together, it forms an arithmetic series.

Review Questions

• How do you find the common difference in an arithmetic sequence?
• Write down 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 series?

Related terms

Geometric Sequence:

A sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called a ratio.

Series:

The sum of the terms of a sequence.

Common Difference:

The constant amount that each term in an arithmetic sequence differs from its preceding term.