Infinite sequence

Definition

An infinite sequence is an ordered list of numbers that continues indefinitely without terminating. Each number in the sequence is called a term, and the position of each term is specified by a positive integer.

5 Must Know Facts For Your Next Test

1. Infinite sequences can be arithmetic or geometric, depending on whether they have a common difference or ratio.
2. The general term of an infinite sequence is often denoted as $a_n$, where $n$ represents the position of the term in the sequence.
3. Convergence and divergence describe whether the terms of an infinite sequence approach a specific value (converge) or not (diverge).
4. Sigma notation ($\sum$) is commonly used to represent the sum of terms in an infinite series derived from an infinite sequence.
5. Infinite sequences can be expressed using recursive formulas, where each term is defined based on preceding terms.

Review Questions

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 constant ratio.

Series:

The sum of all terms in a given sequence.