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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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 explicit formula for an arithmetic sequence?

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The explicit formula for an arithmetic sequence is given by: 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

Front

What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is given by: 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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Example of an arithmetic sequence: 3, 7, 11, 15. What is the common difference?

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The common difference is 4, as each term increases by 4.

Tags

CCSS.HSF.BF.A.2

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Example of a geometric sequence: 2, 6, 18, 54. What is the common ratio?

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The common ratio is 3, as each term is multiplied by 3.

Tags

CCSS.HSF.BF.A.2

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What is the 5th term of the arithmetic sequence: 5, 10, 15, ...?

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The 5th term is 25.

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CCSS.HSF.BF.A.2

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What is the 4th term of the geometric sequence: 3, 9, 27, ...?

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The 4th term is 81.

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CCSS.HSF.BF.A.2