Arithmetic, Geometric, or Neither?

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What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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What is a geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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How do you find the common difference in an arithmetic sequence?

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The common difference is found by subtracting any term from the term that follows it.

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How do you find the common ratio in a geometric sequence?

Back

The common ratio is found by dividing any term by the term that precedes it.

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What is the formula for the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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What is the formula for the nth term of a geometric sequence?

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The nth term of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

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What is the sum of the first n terms of an arithmetic sequence?

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The sum of the first n terms of an arithmetic sequence can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

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What is the sum of the first n terms of a geometric sequence?

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The sum of the first n terms of a geometric sequence can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), for r ≠ 1.

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What is a sequence that is neither arithmetic nor geometric?

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A sequence that does not have a constant difference (arithmetic) or a constant ratio (geometric) is considered neither.

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Provide an example of an arithmetic sequence.

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An example of an arithmetic sequence is: 3, 6, 9, 12, 15 (common difference of 3).