key term - Finite arithmetic sequence

Definition

A finite arithmetic sequence is a sequence of numbers with a definite number of terms in which the difference between consecutive terms is constant. This constant difference is known as the common difference.

5 Must Know Facts For Your Next Test

1. The formula to find the $n$-th term of a finite arithmetic sequence is $a_n = a_1 + (n-1)d$, 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 $S_n = \frac{n}{2} (a_1 + a_n)$ or $S_n = \frac{n}{2} [2a_1 + (n-1)d]$.
3. The common difference, $d$, can be calculated by subtracting any term from its subsequent term: $d = a_{n+1} - a_n$.
4. Finite arithmetic sequences have a specific number of terms, which means they always have both a first and last term.
5. Arithmetic sequences are linear sequences because their graphs form straight lines when plotted.

Review Questions

Related terms

Common Difference:

The constant value that separates consecutive terms in an arithmetic sequence, represented by $d$.

Arithmetic Series:

The sum of all terms in an arithmetic sequence.

$n$-th Term: The specific term located in position $n$ within a sequence, often found using formulas specific to sequences.