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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Define the common difference in an arithmetic sequence.

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The common difference (d) is the constant amount that each term in the sequence increases or decreases by.

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CCSS.HSF.BF.A.2

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How do you find the common difference in a sequence?

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To find the common difference, subtract any term from the subsequent term: d = a_n - a_(n-1).

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CCSS.HSF.BF.A.2

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What is the recursive formula for an arithmetic sequence?

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The recursive formula is given by: a_n = a_(n-1) + d, where d is the common difference.

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CCSS.HSF.BF.A.2

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Write the recursive formula for the sequence: 3, 7, 11, 15,...

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a_1 = 3, a_n = a_(n-1) + 4.

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CCSS.HSF.BF.A.2

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Is the sequence 5, 10, 15, 20,... arithmetic?

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Yes, it is arithmetic with a common difference of 5.

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CCSS.HSF.BF.A.2

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Given a recursive formula a_n = a_(n-1) + 2, what are the first four terms if a_1 = 1?

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1, 3, 5, 7.

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CCSS.HSF.BF.A.2

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What does it mean if a sequence is not arithmetic?

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If a sequence is not arithmetic, it means the difference between consecutive terms is not constant.

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CCSS.HSF.BF.A.2

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Write the recursive formula for the sequence: 20, 15, 10, 5,...

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a_1 = 20, a_n = a_(n-1) - 5.

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CCSS.HSF.BF.A.2

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How can you determine if a sequence is arithmetic?

Back

Calculate the differences between consecutive terms; if they are all the same, the sequence is arithmetic.

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CCSS.HSF.BF.A.2