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Chapter 11 Sequences and Series

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11.1 Arithmetic Sequences

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Key Terms Sequence: an ordered list of numbers 1, 3, 5, 7, 9, …. Terms: the numbers in the sequence The 1 st term in the sequence above is 1, 2 nd is 3, 3 rd is 5, etc Arithmetic Sequence: a sequence in which each terms after the 1 st is found by adding a constant Common difference: the number added to each term in an arithmetic sequence

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Arithmetic sequence Formula: a n = a 1 + (n – 1)d a n = specific term (nth term) a 1 = 1 st term in the sequence n = number of position for given term d = common difference

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Find the next four terms in the sequence. -6, -2, 2,…. 1.6, 1.1, 0.6, ….

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Write an equation for the nth term 10, 7, 4, 1, …

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Write an equation for the nth term 8, 17, 26, 35, …

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The table shows typical costs for a construction company to rent a crane for one, two, three, and four months. If the sequence continues, how much would it cost to rent the crane for a year? The construction company has a budget of $350,000 for crane rental. The job is expected to last 18 months. Will the company be able to afford the crane rental for the entire job? Explain. MonthsCost ($) 175,000 290,000 3105,000 4120,000

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Find the first 5 terms for the sequence described a 1 = 2 d = 13 Find the indicated term for the sequence a 1 = 20, d = 4, n = 81

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Arithmetic Means The terms between any two non- successive terms in an arithmetic sequence Use the formula to find the common difference Then use the common difference to calculate the arithmetic means

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Find the arithmetic means between the given terms 16,__, __, __, __, 91, … 15.6, __, __, __, 60.4,...

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