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10.1 Sequences and Series Fri Nov 1

10.1 Sequences and Series Fri Nov 1. Do Now State the pattern 1) 0, 1, 3, 6, 10, 15, … 2) 1, 1, 2, 3, 5, 8, 13, 21, …. CH ¾ Test review. Retakes by next Wed. Sequences. A finite sequence is a function, where the domain is a set of consecutive positive integers beginning with 1

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10.1 Sequences and Series Fri Nov 1

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  1. 10.1 Sequences and SeriesFri Nov 1 Do Now State the pattern 1) 0, 1, 3, 6, 10, 15, … 2) 1, 1, 2, 3, 5, 8, 13, 21, …

  2. CH ¾ Test review • Retakes by next Wed

  3. Sequences • A finite sequence is a function, where the domain is a set of consecutive positive integers beginning with 1 • An infinite sequence is a function having for its domain the set of all positive integers

  4. Ex • Find the first 4 terms and the 23rd term of the sequence whose general term I given by

  5. Calculators • You can use your graphing calculator to see the terms of a sequence • 1) Type the expression in Y= • 2) 2nd -> table

  6. Graphs of Sequences • The graph of a sequence mimics the graph of the identical function, except only the x integers are plotted • Ex: f(x) = x + 1 and a = n + 1

  7. Finding the general term • To find the general term, we need to find the pattern and make a prediction. • Remember: you will always plug in n = 1 first • Ex: • 1) • 2) -1, 3, -9, 27, -81, … • 3) 2, 4, 8, 16, …

  8. Recursive Sequences • A sequence may be defined recursively, which uses the previous term to find the new term • Ex: Find the first 5 terms of the sequence defined by

  9. Closure • Find the first 4 terms, and the 10th term of the sequence • HW: p.850 #1-27 odds 61 65 71

  10. 10.1 Sums and SeriesMon Nov 4 • Do Now • Find the first 4 terms of the sequence, then add them together

  11. HW Review: p.850 #1-27 61 65 71

  12. Series • A series is the sum of a sequence. • An infinite series is the sum of the terms of an infinite sequence • A finite series, or partial sum, is the sum of the first n terms of a sequence • A finite series, or nth partial sum, is denoted

  13. Ex • For the sequence -2, 4, -6, 8, -10, 12, -14,…, find each of the following • 1) • 2) • 3)

  14. Sigma Notation • The Greek letter sigma is used to represent a partial sum or series. This is called sigma notation

  15. Ex • Find and evaluate each of the following sums • 1) • 2)

  16. Ex • Write sigma notation for each sum • 1) 1 + 2 + 4 + 8 + 16 + 32 + 64 • 2) -2 + 4 – 6 + 8 – 10 • 3)

  17. Closure • Find and evaluate the sum HW: p. 850 #29-59 odds

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