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Patterns and sequences
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Patterns and sequences

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Presentation on sequences that are Arithmetic, Geometric, and neither.

Presentation on sequences that are Arithmetic, Geometric, and neither.

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  • 1.  
  • 2.
    • The constant amount between terms in an arithmetic sequence is called the common difference . We add the common difference to get to the next term.
    • Would the common difference be a positive or a negative number in a sequence that went down?
    • For example, what is the common difference in this sequence?
            • 11, 9, 7, 5, 3, …
  • 3.
    • Try writing a rule for this sequence:
            • 2, 5, 8, 11, …
    • It starts with: ________
    • It goes up by: _________
    • Again, each term of an arithmetic sequence goes up by a fixed amount, which is called the ____________________.
  • 4.
    • Each term of a geometric sequence is found by multiplying the previous term by a fixed number. This ratio is called the common ratio .
    • Would the common ratio be a whole number or a fraction in a sequence that went down?
    • Identify the common ratio in this sequence…
    • 27, 9, 3, 1, ……..
  • 5.
    • Sequences are neither arithmetic or geometric when they have no common difference or ratio.
    • For example, look at this sequence…
    • 1, 4, 9, 16, 25, …
    • What is the rule for this sequence? Why is it not an arithmetic or geometric sequence?
  • 6.
    • Here is an another example of a sequence that is neither arithmetic or geometric:
    • You can use algebraic expressions to describe the terms of many different sequences...
  • 7.
    • 4, 12, 20, 28, 36, …
    • Is it an arithmetic sequence, geometric sequence, or neither ?
    • What is the common difference or common ratio of this sequence?
    • The next three terms are: .
  • 8.
    • 10, 11, 13, 16, 20, …
    • Is it an arithmetic sequence, geometric sequence, or neither ?
    • What is the common difference or common ratio of this sequence?
    • The next three terms are: .
  • 9.
    • 3, -9, 27, -81, 243, …
    • Is it an arithmetic sequence, geometric sequence, or neither ?
    • What is the common difference or common ratio of this sequence?
    • The next three terms are: .
  • 10.
    • 4, -1, -6, -11, -16, …
    • Is it an arithmetic sequence, geometric sequence, or neither ?
    • What is the common difference or common ratio of this sequence?
    • The next three terms are: .
  • 11.
    • 1, 0, 2, 0, 3, …
    • Is it an arithmetic sequence, geometric sequence, or neither ?
    • What is the common difference or common ratio of this sequence?
    • The next three terms are: .
  • 12.
    • 100, 20, 4, 0.8, 0.16, …
    • Is it an arithmetic sequence, geometric sequence, or neither ?
    • What is the common difference or common ratio of this sequence?
    • The next three terms are: .