Finite sequence

Definition

A finite sequence is an ordered list of numbers with a definite number of terms. Each term in the sequence is indexed by a positive integer.

5 Must Know Facts For Your Next Test

1. A finite sequence has a specific starting and ending point.
2. The general form of a finite sequence can be denoted as $(a_1, a_2, ..., a_n)$ where $n$ is the number of terms.
3. Finite sequences can be arithmetic, geometric, or neither.
4. The sum of the terms in a finite sequence can often be calculated using specific formulas.
5. In notation, $a_i$ represents the $i$-th term in the sequence.

Review Questions

• What defines the boundaries of a finite sequence?
• How do you denote the general form of a finite sequence?
• Can you identify whether a given sequence is arithmetic or geometric?

Related terms

Arithmetic Sequence: A sequence in which each term after the first is obtained by adding a constant difference to the previous term.

Geometric Sequence: A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Series: The sum of the terms of a sequence.