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# Discrete Mathematics Section 1.2 - PowerPoint PPT Presentation

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, _____

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### Discrete Mathematics Section 1.2

Number Puzzles and Sequences

Guess the next number Discovering Patterns in Sequences

• 1, 3, 5, 7, 9, _____

• 1, 4, 9, 16, 25, 36, ______

Finding a Pattern Discovering Patterns in Sequences

• 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.

Finding a Pattern Discovering Patterns in Sequences

• 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.

Finding a Pattern Discovering Patterns in Sequences

• 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.

Three Ways to Describe a Sequence Discovering Patterns in Sequences

• 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.

Pascal’s Triangle Discovering Patterns in Sequences

Pascal’s Triangle Left-Aligned Discovering Patterns in Sequences

Pascal’s Triangle Left- and Top-Aligned Discovering Patterns in Sequences

Consider the Columns as Sequences Discovering Patterns in Sequences