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Published byBlake Beasley Modified over 9 years ago
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This Slideshow was developed to accompany the textbook Larson Algebra 2 By Larson, R., Boswell, L., Kanold, T. D., & Stiff, L. 2011 Holt McDougal Some examples and diagrams are taken from the textbook. Slides created by Richard Wright, Andrews Academy rwright@andrews.edu Slides created by Richard Wright, Andrews Academy rwright@andrews.edu
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Sequence Function whose domain are integers List of numbers that follow a rule 2, 4, 6, 8, 10 Finite 2, 4, 6, 8, 10, … Infinite
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To graph n is like x; a n is like y The graph will be dots Do NOT connect the dots
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Series Sum of a sequence 2, 4, 6, 8, … sequence 2 + 4 + 6 + 8 + · · · series
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Index of summation (variable) Lower limit Upper limit
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12.1 Homework Quiz 12.1 Homework Quiz
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Arithmetic Sequences Common difference (d) between successive terms Add the same number each time 3, 6, 9, 12, 15, … d = 3 Is it arithmetic? -10, -6, -2, 0, 2, 6, 10, … 5, 11, 17, 23, 29, …
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Write a rule for the n th term 32, 47, 62, 77, … Formula for n th term a n = a 1 + (n – 1)d
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One term of an arithmetic sequence is a 8 = 50. The common difference is 0.25. Write the rule for the n th term.
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Two terms of an arithmetic sequence are a 5 = 10 and a 30 = 110. Write a rule for the n th term.
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Consider the arithmetic series 20 + 18 + 16 + 14 + ··· Find the sum of the first 25 terms.
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Consider the arithmetic series 20 + 18 + 16 + 14 + ··· Find n such that S n = -760 806 #3-63 every other odd, 65 + 3 = 20
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12.2 Homework Quiz 12.2 Homework Quiz
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Created by multiplying by a common ratio (r) Are these geometric sequences? 1, 2, 6, 24, 120, … 81, 27, 9, 3, 1, …
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Write a rule for the n th term and find a 8. 5, 2, 0.8, 0.32, … Formula for n th term a n = a 1 ·r n-1
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One term of a geometric sequence is a 4 = 3 and r = 3. Write the rule for the n th term.
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If two terms of a geometric sequence are a 2 = -4 and a 6 = -1024, write rule for the n th term.
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Find the sum of the first 10 terms of 4 + 2 + 1 + ½ + ···
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Find n such that S n = 31/4 4 + 2 + 1 + ½ + ··· 814 #3-47 every other odd, 49, 51, 53, 57, 59 + 3 = 20
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12.3 Homework Quiz 12.3 Homework Quiz
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What is the sum of the pieces if we keep cutting forever?
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An infinite geometric series has a 1 = 5 has sum of 27/5. Find the common ratio.
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Write 0.27272727… as a fraction.
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Write 0.416666666… as a fraction. 823 #3-33 odd, 37, 39, 42 + 1 = 20
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12.4 Homework Quiz 12.4 Homework Quiz
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Explicit Rule Gives the n th term directly a n = 2 + 4n Recursive Rule Each term is found by knowing the previous term a 1 = 6; a n = a n-1 + 4
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a 1 = 2, a 2 = 2, a n = a n-2 – a n-1 Write the first 5 terms a 1 = 1, a n = (a n-1 ) 2 + 1
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Write the rules for the arithmetic sequence where a 1 = 15 and d = 5. Explicit Recursive
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Write the rule for the geometric sequence where a 1 = 4 and r = 0.2 Explicit Recursive
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1, 2, 2, 4, 8, 32, … Write a recursive rule for 1, 1, 4, 10, 28, 76, …
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Iterations Repeated composition of functions f(f(f(x))) Use x to find f(x) Use that value to find the next f(x) x 1 = f(x 0 ); x 2 = f(x 1 ), … Find the first three iterations of the function. f(x) = 4x – 3, x 0 = 2 830 #3-31 odd, 35-39 odd, 43, 45 + 5 = 25
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12.5 Homework Quiz 12.5 Homework Quiz
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843 #choose 20 = 20
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