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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CCSS.HSF.BF.A.2

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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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What is the explicit formula for an arithmetic sequence?

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The explicit formula for 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 explicit formula for a geometric sequence?

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The explicit formula for 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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How do you find the common difference in an arithmetic sequence?

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The common difference (d) can be found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

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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 (r) can be found by dividing any term by the previous term: r = a_(n+1) / a_n.

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CCSS.HSF.BF.A.2

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What is the value of a_22 in the sequence defined by a_n = 5 - 3n?

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a_22 = 5 - 3(22) = 5 - 66 = -61.

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CCSS.HSF.BF.A.2

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Identify whether the sequence {14, 22, 30, 38, ...} is arithmetic, geometric, or neither.

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The sequence is arithmetic because the difference between consecutive terms is constant (8).

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CCSS.HSF.BF.A.2

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Which of the following sequences is arithmetic: 3, 6, 2, 7 or 3, 7, 11, 15?

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3, 7, 11, 15 is an arithmetic sequence because the common difference is 4.

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CCSS.HSF.BF.A.2

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What is a term in a sequence?

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A term in a sequence is an individual number or element of the sequence.

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