An arithmetic sequence has a constant difference between its terms, while a non-arithmetic sequence does not. Here are some examples to clarify the difference:
Arithmetic Sequence
An arithmetic sequence is a series of numbers where the difference between any two consecutive terms remains constant.
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Example 1: 21, 16, 11, 6, ...
- In this sequence, each term is 5 less than the previous term. The common difference is -5. As noted in the Intro to arithmetic sequences | Algebra (article) - Khan Academy, this sequence is arithmetic because the difference between consecutive terms is always minus five.
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Key Feature: A consistent difference between consecutive terms.
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General Form: a, a+d, a+2d, a+3d,..., where a is the first term and d is the common difference.
Not Arithmetic Sequence
A sequence that does not have a constant difference between its consecutive terms is not an arithmetic sequence.
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Example 1: 1, 2, 4, 8, ...
- In this sequence, each term is multiplied by 2 to get the next term. The differences between the terms are 1, 2, and 4. Since the differences are not the same, as stated in the reference Intro to arithmetic sequences | Algebra (article) - Khan Academy, this sequence is not arithmetic.
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Key Feature: The difference between consecutive terms is not constant.
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General Form: There's no consistent formula applicable to all non-arithmetic sequences. They can be geometric, exponential, or follow other patterns.
Comparison Table
| Feature | Arithmetic Sequence | Not Arithmetic Sequence |
|---|---|---|
| Common Difference | Has a constant difference between consecutive terms | Does not have a constant difference between consecutive terms |
| Example | 21, 16, 11, 6,... (common difference is -5) | 1, 2, 4, 8,... (no common difference) |
In summary, arithmetic sequences involve adding or subtracting a fixed value each time, while non-arithmetic sequences can involve other operations or have variable patterns.
