Patterns and Sequences

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Patterns and Sequences

• Henrico County Public School
• Mathematics Teachers

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Patterns and Sequences

• Patterns refer to usual types of procedures or
  rules that can be followed.
• Patterns are useful to predict what came before
  or what might come after a set a numbers that are
  arranged in a particular order.
• This arrangement of numbers is called a sequence.
• For example 3,6,9,12 and 15 are numbers that
  form a pattern called a sequence.
• The numbers that are in the sequence are called
  terms.

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Patterns and Sequences

• Arithmetic sequence (arithmetic progression) a
  sequence of numbers in which the difference
  between any two consecutive numbers or
  expressions is the same
• Geometric sequence a sequence of numbers in
  which each term is formed by multiplying the
  previous term by the same number or expression

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Arithmetic Sequence 1
Find the next three numbers or terms in each
pattern.

• Look for a pattern usually a procedure or rule
  that uses the same number or expression each time
  to find the next term. The pattern is to add 5
  to each term.

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The Next Three Numbers

• Add five to the last term
• The next three terms are

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Arithmetic Sequence 2
Find the next three numbers or terms in each
pattern.

• Look for a pattern usually a procedure or rule
  that uses the same number or expression each time
  to find the next term. The pattern is to add the
  integer (-3) to each term.

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The Next Three Numbers 2

• Add the integer (-3) to each term
• The next three terms are

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Geometric Sequence 1
Find the next three numbers or terms in each
pattern.

• Look for a pattern usually a procedure or rule
  that uses the same number or expression each time
  to find the next term. The pattern is to
  multiply each term by three.

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The Next Three 1

• Multiply each term by three
• The next three terms are

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Geometric Sequence 2
Find the next three numbers or terms in each
pattern.

• Look for a pattern usually a procedure or rule
  that uses the same number or expression each time
  to find the next term. The pattern is to divide
  each term by two.

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The Next Three 2

• Divide each term by two
• The next three terms are

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Note

• To divide by a number is the same as multiplying
  by its reciprocal.
• The pattern for a geometric sequence is
  represented as a multiplication pattern.
• For example to divide by 2 is represented as the
  pattern multiply by a half.

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Patterns Sequences
Decide the pattern for each and find the next
three numbers.
a) 7, 12, 17, 22, b) 1, 4, 7, 10, c) 2, 6,
18, 54, ... d) 20, 18, 16, 14, e) 64, 32, 16,
...
a) 27, 32, 37 b) 13, 16, 19 c) 162, 486,
1548 d) 12, 10, 8 e) 8, 4, 2