Arithmetic and Geometric Sequences

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What is an Arithmetic Sequence?

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

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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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CCSS.HSF.BF.A.2

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

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The common difference can be found by subtracting any term from the term that follows it. For example, in the sequence 3, 7, 11, the common difference is 7 - 3 = 4.

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CCSS.HSF.BF.A.2

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

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The common ratio can be found by dividing any term by the term that precedes it. For example, in the sequence 2, 6, 18, the common ratio is 6 / 2 = 3.

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CCSS.HSF.BF.A.2

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

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

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CCSS.HSF.BF.A.2

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

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

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CCSS.HSF.BF.A.2

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Is the sequence {2, 9, 7, 14, 12, 19, ...} arithmetic, geometric, or neither?

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Neither.

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CCSS.HSF.BF.A.2

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What is the common difference of the sequence 97, 86, 75, 64, ...?

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-11.

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CCSS.HSF.BF.A.2

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What is the common ratio of the geometric sequence 5, 25, 125, 625...?

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5.

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CCSS.HSF.BF.A.2

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Which type of sequence has a common ratio?

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Geometric.

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