patterns and sequences
DESCRIPTION
Presentation on sequences that are Arithmetic, Geometric, and neither.TRANSCRIPT
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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, …
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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 ____________________.
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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, ……..
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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?
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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...
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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: .
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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: .
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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: .
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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: .
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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: .
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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: .