DNB: Recursive Formula

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What is a recursive formula?

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A recursive formula defines each term of a sequence using the preceding term(s). It typically includes an initial condition and a rule for generating subsequent terms.

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CCSS.HSF.BF.A.2

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What is the initial term in a recursive sequence?

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The initial term is the first term of the sequence, often denoted as a_1.

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CCSS.HSF.BF.A.2

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How do you express a recursive formula for a sequence that decreases by a constant value?

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If a sequence decreases by a constant value, the recursive formula can be expressed as a_n = a_{n-1} - d, where d is the constant decrease.

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CCSS.HSF.BF.A.2

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How do you express a recursive formula for a sequence that increases by a constant value?

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If a sequence increases by a constant value, the recursive formula can be expressed as a_n = a_{n-1} + d, where d is the constant increase.

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CCSS.HSF.BF.A.2

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What is 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

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What is the recursive formula for the sequence 7, 14, 28, 56, 112,...?

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a_1 = 7, a_n = a_{n-1} \cdot 2.

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CCSS.HSF.BF.A.2

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What is the recursive formula for the sequence 1, 3, 9, 27,...?

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a_n = a_{n-1} \cdot 3.

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CCSS.HSF.IF.A.3

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What is the difference between a recursive formula and an explicit formula?

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A recursive formula defines terms based on previous terms, while an explicit formula provides a direct way to calculate the nth term without referencing previous terms.

Tags

CCSS.HSF.BF.A.2

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What is the role of the initial condition in a recursive formula?

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The initial condition provides the starting point for the sequence, allowing the recursive formula to generate subsequent terms.

Tags

CCSS.HSF.BF.A.2

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How can you identify the pattern in a recursive sequence?

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To identify the pattern, examine the differences or ratios between consecutive terms to determine if the sequence is arithmetic, geometric, or follows another rule.

Tags

CCSS.HSF.BF.A.2