Sequences & Recursive Formula

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What is a sequence in mathematics?

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A sequence is an ordered list of numbers that follow a specific pattern or rule.

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CCSS.HSF.BF.A.2

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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 recursive formula?

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A recursive formula defines each term of a sequence using the previous term(s).

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CCSS.HSF.BF.A.2

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What is an explicit formula?

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An explicit formula allows you to find the nth term of a sequence directly without needing to know the previous terms.

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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 is found by subtracting any term from the term that follows it.

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CCSS.HSF.BF.A.2

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Given the sequence 2, 8, 14, what is the common difference?

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The common difference is 6.

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CCSS.HSF.BF.A.2

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What is the first term of the sequence defined by f(n)=f(n-1)+6 and f(1)=2?

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The first term is 2.

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CCSS.HSF.IF.A.3

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How do you calculate f(7) in the sequence defined by f(n)=f(n-1)+15 and f(1)=15?

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f(7) = 15 + 15*6 = 105.

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CCSS.HSF.IF.A.3

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What is the next term in the series 15, 35, 55?

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The next term is 75.

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CCSS.HSF.BF.A.2

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If f(n)=f(n-1)+2 and f(1)=0, what is f(5)?

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f(5) = 0 + 2*4 = 8.

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CCSS.HSF.IF.A.3