Arithmetic Sequences/Recursive Formula

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

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The common difference (d) can be found by subtracting any term from the subsequent term in the sequence.

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CCSS.HSF.BF.A.2

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Given the sequence 5, 10, 15, 20, what is the common difference?

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The common difference is 5.

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CCSS.HSF.BF.A.2

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What is the nth term formula for an arithmetic sequence?

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The nth term (a_n) of an arithmetic sequence can be calculated 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

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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).

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CCSS.HSF.BF.A.2

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Given the recursive formula a_n = a_{n-1} + 3, what is a_4 if a_1 = 2?

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a_4 = 2 + 3 + 3 + 3 = 11.

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CCSS.HSF.BF.A.2

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What is the explicit formula for the arithmetic sequence 2, 5, 8, 11?

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The explicit formula is a_n = 2 + (n-1)3.

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CCSS.HSF.BF.A.2

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How do you determine if a sequence is arithmetic?

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A sequence is arithmetic if the difference between consecutive terms is constant.

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CCSS.HSF.BF.A.2

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What are the first four terms of the sequence defined by a_1 = 50 and a_n = a_{n-1} - 5?

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The first four terms are 50, 45, 40, 35.

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CCSS.HSF.BF.A.2

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If the first term of an arithmetic sequence is 10 and the common difference is -2, what is the 5th term?

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The 5th term is 10 + (5-1)(-2) = 10 - 8 = 2.

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CCSS.HSF.BF.A.2