Recursive and Arithmetic Sequences

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What is a recursive sequence?

Back

A recursive sequence is a sequence of numbers where each term is defined as a function of one or more of the preceding terms.

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CCSS.HSF.IF.A.3

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What is the first term of the sequence defined by a_n = a_{n-1} + 5 with a_1 = -16?

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The first term is -16.

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CCSS.HSF.BF.A.2

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How do you find the first four terms of a recursive sequence?

Back

Start with the first term and use the recursive formula to calculate subsequent terms.

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CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the constant amount that each term increases or decreases by.

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CCSS.HSF.BF.A.2

Front

Write the recursive formula for the sequence 10, 5, 0, -5,...

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a_1 = 10, a_n = a_{n-1} - 5.

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CCSS.HSF.BF.A.2

Front

What is the explicit formula for an arithmetic sequence?

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The explicit formula is a_n = a_1 + (n-1)d, where d is the common difference.

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CCSS.HSF.BF.A.2

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Given the sequence 15, 12, 9, 6, 3, what is the recursive formula?

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a_1 = 15, a_n = a_{n-1} - 3.

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CCSS.HSF.BF.A.2

Front

How do you determine the next term in a sequence?

Back

Use the recursive formula or the explicit formula to calculate the next term.

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CCSS.HSF.BF.A.2

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What does the slope represent in the context of a linear equation related to sequences?

Back

The slope represents the common difference in an arithmetic sequence.

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If a_n = 7 in the sequence 2, 7, 12, 17,..., what is a_{n+1}?

Back

a_{n+1} = 12.

Tags

CCSS.HSF.BF.A.2