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Published byTheresa Young Modified over 7 years ago

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Arithmetic Sequences ~adapted from Walch Education

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Arithmetic sequences An arithmetic sequence is a list of terms separated by a common difference, the number added to each consecutive term in an arithmetic sequence. An arithmetic sequence is a linear function with a domain of positive consecutive integers in which the difference between any two consecutive terms is equal. The rule for an arithmetic sequence can be expressed either explicitly or recursively.

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Arithmetic sequences, continued. The explicit rule for an arithmetic sequence is a n = a 1 + (n – 1)d, where a 1 is the first term in the sequence, n is the term, d is the common difference, and a n is the nth term in the sequence. The recursive rule for an arithmetic sequence is a n = a n – 1 + d, where a n is the nth term in the sequence, a n – 1 is the previous term, and d is the common difference.

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Practice Write a linear function that corresponds to the following arithmetic sequence. ▫8, 1, –6, –13, …

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Solve the Problem: Find the common difference by subtracting two successive terms. 1 – 8 = –7 Identify the first term (a1). a 1 = 8 Write the explicit formula. a n = a 1 + (n – 1)d a n = 8 + (n – 1)(–7)

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Write the formula in function notation. Simplify the explicit formula a n = 8 – 7n + 7 a n = –7n + 15 ƒ(x) = –7x + 15 Note: the domain of an arithmetic sequence is positive consecutive integers.

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~Dr. Dambreville

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