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. For example, {2, 5, 8, 11, ...} has a common difference of 3.

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CCSS.HSF.BF.A.2

Front

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. For example, {3, 6, 12, 24, ...} has a common ratio of 2.

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CCSS.HSF.BF.A.2

Front

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: 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

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

Back

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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CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

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The common difference is the fixed amount that each term increases or decreases by in an arithmetic sequence. It is calculated by subtracting any term from the subsequent term.

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CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

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

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CCSS.HSF.BF.A.2

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Identify whether the sequence {5, 10, 15, 20, ...} is arithmetic, geometric, or neither.

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The sequence {5, 10, 15, 20, ...} is arithmetic because the common difference is 5.

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CCSS.HSF.BF.A.2

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Identify whether the sequence {2, 4, 8, 16, ...} is arithmetic, geometric, or neither.

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The sequence {2, 4, 8, 16, ...} is geometric because the common ratio is 2.

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CCSS.HSF.BF.A.2

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What is the 10th term of the arithmetic sequence {3, 7, 11, ...}?

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The 10th term is 39.

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CCSS.HSF.BF.A.2

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What is the 6th term of the geometric sequence {1, 3, 9, 27, ...}?

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The 6th term is 729.

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CCSS.HSF.BF.A.2