Sequence

Definition

A sequence is an ordered list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term.

5 Must Know Facts For Your Next Test

1. A sequence can be finite or infinite.
2. The general term of a sequence is often denoted as $a_n$ where $n$ is the position of the term.
3. In an arithmetic sequence, each term after the first is obtained by adding a constant difference to the preceding term.
4. The sum of the first $n$ terms of an arithmetic sequence is given by $S_n = \frac{n}{2}(a_1 + a_n)$.
5. Recognizing patterns in sequences can help solve problems related to series and summation.

Review Questions

• What defines an arithmetic sequence?
• How do you find the nth term of an arithmetic sequence?
• What is the formula for the sum of the first n terms of an arithmetic sequence?

Related terms

Arithmetic Sequence:

A type of sequence where each term differs from the previous one by a constant amount.

Geometric Sequence:

A type of sequence where each term is obtained by multiplying the previous term by a constant factor.

Series:

The sum of the terms in a sequence.