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 in which the ratio between consecutive terms is constant. This ratio is called the common ratio.

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CCSS.HSF.BF.A.2

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How do you find the nth term of an arithmetic sequence?

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

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CCSS.HSF.BF.A.2

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How do you find the nth term of a geometric sequence?

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

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CCSS.HSF.BF.A.2

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What is the common difference in an arithmetic sequence?

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The common difference in an arithmetic sequence is the fixed amount that each term increases or decreases by from the previous term.

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CCSS.HSF.BF.A.2

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What is the common ratio in a geometric sequence?

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The common ratio in a geometric sequence is the fixed factor by which each term is multiplied to get the next term.

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CCSS.HSF.BF.A.2

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Provide an example of an arithmetic sequence.

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An example of an arithmetic sequence is 2, 5, 8, 11, 14, ... (with a common difference of 3).

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CCSS.HSF.BF.A.2

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Provide an example of a geometric sequence.

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An example of a geometric sequence is 3, 6, 12, 24, 48, ... (with a common ratio of 2).

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CCSS.HSF.BF.A.2

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What is a recursive formula for an arithmetic sequence?

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A recursive formula for an arithmetic sequence can be expressed as: f(1) = a, f(n) = f(n-1) + d.

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CCSS.HSF.BF.A.2

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What is a recursive formula for a geometric sequence?

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A recursive formula for a geometric sequence can be expressed as: f(1) = a, f(n) = f(n-1) * r.

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