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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, _____

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Discrete Mathematics Section 1.2

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  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

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