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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

Discrete Mathematics Section 1.2

Number Puzzles and Sequences



Guess the next number
Guess the next number Discovering Patterns in Sequences

  • 1, 3, 5, 7, 9, _____

  • 1, 4, 9, 16, 25, 36, ______


Finding a pattern
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 pattern1
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 pattern2
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
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
Pascal’s Triangle Discovering Patterns in Sequences


Pascal s triangle left aligned
Pascal’s Triangle Left-Aligned Discovering Patterns in Sequences


Pascal s triangle left and top aligned
Pascal’s Triangle Left- and Top-Aligned Discovering Patterns in Sequences


Consider the columns as sequences
Consider the Columns as Sequences Discovering Patterns in Sequences


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