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.

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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 formula for 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

What is the formula for 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

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

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The common difference (d) is found by subtracting any term from the subsequent term: d = a(n+1) - a(n).

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CCSS.HSF.BF.A.2

Front

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

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The common ratio (r) is found by dividing any term by the previous term: r = a(n) / a(n-1).

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CCSS.HSF.BF.A.2

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What is the 10th term of the sequence a(n) = 20 - 2n?

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0

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CCSS.HSF.BF.A.2

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What are the individual numbers in a sequence called?

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Terms.

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CCSS.HSF.BF.A.2

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If f(x) = -9x + 12, what is f(20)?

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-168

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CCSS.HSF.IF.A.2

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Identify the common difference in the sequence: 97, 86, 75, 64, ...

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-11

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CCSS.HSF.BF.A.2