Chapter 11 Sequences and Series. 11.1 Arithmetic Sequences.

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Presentation transcript:

Chapter 11 Sequences and Series

11.1 Arithmetic Sequences

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

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

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

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

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

 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

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

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

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