key term - Ellipsis

Definition

An ellipsis is a notation consisting of three dots ($\ldots$) used to indicate the continuation of a sequence. It implies that the pattern established by the preceding terms continues in a consistent manner.

5 Must Know Facts For Your Next Test

1. Ellipses are often used to represent infinite sequences or long finite sequences where listing every term is impractical.
2. In arithmetic sequences, ellipses help indicate that each term increases by a constant difference.
3. For geometric sequences, ellipses show that each term is multiplied by a constant ratio from the previous term.
4. Ellipses can be used in summation notation to denote that intermediate steps have been omitted for brevity.
5. When using an ellipsis in set notation, it implies the elements follow a predictable pattern.

Review Questions

Related terms

Arithmetic Sequence:

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

Geometric Sequence:

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

Summation Notation: $\sum$ notation represents the sum of terms in a sequence, often using an index to specify which terms are included.