1 / 11

Discrete Mathematics Section 1.2

Discrete Mathematics Section 1.2. Number Puzzles and Sequences. Guess the next number, Sequences and Sequence Notation, & Discovering Patterns in Sequences. Guess the next number. 1, 3, 5, 7, 9, _____ 1, 4, 9, 16, 25, 36, ______. Finding a Pattern. 1, 3, 5, 7, 9, _____

nhi
Download Presentation

Discrete Mathematics Section 1.2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discrete Mathematics Section 1.2 Number Puzzles and Sequences

  2. Guess the next number, Sequences and Sequence Notation, & Discovering Patterns in Sequences

  3. Guess the next number • 1, 3, 5, 7, 9, _____ • 1, 4, 9, 16, 25, 36, ______

  4. Finding a Pattern • 1, 3, 5, 7, 9, _____ • 1, 4, 9, 16, 25, 36, ______ Finding a pattern means one of these three things: • Each term is related (by mathematical operations) to previous terms. • Each term can be described relative to its position in the sequence. • The sequence merely enumerates a set of integers that the reader may recognize.

  5. Finding a Pattern • 1, 3, 5, 7, 9, _____ • 1, 4, 9, 16, 25, 36, ______ Finding a pattern means one of these three things: • Each term is related (by mathematical operations) to previous terms. • Each term can be described relative to its position in the sequence. • The sequence merely enumerates a set of integers that the reader may recognize.

  6. Finding a Pattern • 1, 3, 5, 7, 9, _____ • 1, 4, 9, 16, 25, 36, ______ Finding a pattern means one of these three things: • Each term is related (by mathematical operations) to previous terms. (recursive formula) • Each term can be described relative to its position in the sequence. (closed formula) • The sequence merely enumerates a set of integers that the reader may recognize.

  7. Three Ways to Describe a Sequence • A recursive formula for a sequence is a formula where each term is described in relation to a previous term (or terms) of the sequence. This type of description must include enough information on how the list begins to determine every subsequent term in the list. • A closed formula for a sequence is a formula where each term is described only in relation to position in the list. • We can also describe a sequence in terms of recognition (i.e., the odd positive integers). This is by far the least meaningful description.

  8. Pascal’s Triangle

  9. Pascal’s Triangle Left-Aligned

  10. Pascal’s Triangle Left- and Top-Aligned

  11. Consider the Columns as Sequences

More Related