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Warm-Up Question

Warm-Up Question. Find next three numbers of each list of numbers by identifying the pattern. 1, 2, 3, 4, … 2, 4, 6, 8, … 5, 8, 11, 14, … 14, 10, 6, 2, … 2, 4, 8, 16, … 27, 9, 3, 1, … 1, 1, 2, 3, 5, 8, … 1, 3, 7, 15, 31, …. Sequences and Series. Definition of Sequences and Series.

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Warm-Up Question

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  1. Warm-Up Question Find next three numbers of each list of numbers by identifying the pattern. 1, 2, 3, 4, … 2, 4, 6, 8, … 5, 8, 11, 14, … 14, 10, 6, 2, … 2, 4, 8, 16, … 27, 9, 3, 1, … 1, 1, 2, 3, 5, 8, … 1, 3, 7, 15, 31, …

  2. Sequences and Series Definition of Sequences and Series

  3. Definition of Sequences Lesson: P.434 Sequence is a function whose domain is a set of consecutive integers starting with 1 unless specified. The values in the range are called the terms of the sequence. Domain: 1 2 3 4 5 6 … n Position of each term Range: Terms of the sequence Examples) 1 2 3 4 5 6 … 100 1 2 3 4 5 6 … 100 1 2 3 4 5 6 … 100 2 4 6 8 10 12 … 200

  4. Terms of sequences Lesson: P.434 Write the first four terms of each sequence. Required Practice: P.434 G.P. 1, 2, 3 Additional Practice: P.438 7, 9, 11, 13

  5. Rules of Sequences Lesson: P.435 Describe the pattern, write the next term, and write a rule for the nth term of each sequence. a) -1, -8, -27, -64 b) 0, 2, 6, 12 Required Practice: P.438 15, 16 Additional Practice: P.438 19, 20

  6. Warm-Up Question (9C) Describe the pattern, write the next term, and write a rule for the nth term of each sequence. 1, 3, 5, 7, 9, … 4, 7, 10, 13, 16, … 5, 1, -3, -7, -11, … 13, 11, 9, 7, 5, …

  7. Warm-Up Question (9AB) Calculate each sum. 1+ 2 = ? 1 + 2 + 3 = ? 1 + 2 + 3 + 4 = ? 1 + 2 + 3 + 4 + 5 = ? 1 + 2 + 3 + 4 + 5 + … + 99 + 100 = ? 2 + 4 = ? 2 + 4 + 6 = ? 2 + 4 + 6 + 8 = ? 2 + 4 + 6 + 8 + 10 = ? 2 + 4 + 6 + 8 + 10 + … + 98 + 100 = ?

  8. Definition of Series Lesson: P.434 When the terms of a sequence are added together, the resulting expression is a series. Sequence: 1 2 3 4 5 6 … n 2 4 6 8 10 12 … n 1 + 2 + 3 + 4 + 5 + 6 + … + n 2 + 4 + 6 + 8 + 10 + 12 + … + n Series:1 3 6 10 15 21 ... 2 6 12 20 30 32 …

  9. Summation Notation Lesson: P.436 Summation notation is often used to write a series. 4: Upper limit of summation 2i: Rule for each term. ∑: Greek letter Sigma to notate summation = 2 + 4 + 6 + 8 1: Lower limit of summation i: Index of summation Ex) Write the series using summation notation. a. 25 + 50 + 75 + … + 250 b. Required Practice: P.436 6, 7, 8, 9 Additional Practice: P.438 39, 40, 43

  10. Sum of a Series Lesson: P.437 Find the sum of the series Required Practice: P.437G.P. 10, 11 Additional Practice: P.439 45, 47, 49

  11. Formula for Special Series Lesson: P.437 Sum of n terms of 1 Sum of first n positive integers Sum of squares of first n positive integers Ex) Find the sum of the series Required Practice: P.437G.P. 12, 13 Additional Practice: P. 439 53, 55, 56

  12. Homework Assignment

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