Term

Definition

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

5 Must Know Facts For Your Next Test

1. The general form of a sequence is $a_n$, where $n$ represents the position of the term in the sequence.
2. A sequence can be finite or infinite, depending on whether it has a last term.
3. Arithmetic sequences have a constant difference between consecutive terms, while geometric sequences have a constant ratio.
4. Convergence and divergence characterize whether an infinite sequence approaches a specific value (converges) or not (diverges).
5. Recursive sequences define each term based on previous terms using a recurrence relation.

Review Questions

• What distinguishes an arithmetic sequence from a geometric sequence?
• How can you determine if an infinite sequence converges or diverges?
• What is the general form of a recursive sequence?

Related terms

Arithmetic Sequence:

A type of sequence in which each term after the first is obtained by adding a constant difference to the previous term.

Geometric Sequence:

A type of sequence in which each term after the first is obtained by multiplying the previous term by a constant ratio.

Convergence:

\text{Describes} when an infinite sequence approaches and tends to settle at a specific value as $n$ approaches infinity.