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Algebra II Honors—Day 69

Algebra II Honors—Day 69. Warmup. Solve and check: Find the next four terms of this arithmetic sequence: 207, 194, 181, . . . Find the indicated term of this arithmetic sequence:. Warmup. Check both solutions!!!. -13. -13. -13. -13. Warmup.

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Algebra II Honors—Day 69

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  1. Algebra II Honors—Day 69

  2. Warmup • Solve and check: • Find the next four terms of this arithmetic sequence: 207, 194, 181, . . . • Find the indicated term of this arithmetic sequence:

  3. Warmup Check both solutions!!!

  4. -13 -13 -13 -13 Warmup • Find the next four terms of this arithmetic sequence: 207, 194, 181, . . . What is the common difference?? (194-207=-13 and 181-194=-13, so d=-13) 207, 194, 181, 168, 155, 142, 129

  5. Warmup • Find the indicated term of this arithmetic sequence:

  6. Today Finish up Arithmetic Sequences and Series Essential Question/New Material Homework

  7. Essential Questions What is an arithmetic series and how is it calculated? What is a geometric sequence? What is a geometric series, and how is it calculated?

  8. UPPER BOUND (NUMBER) SIGMA (SUM OF TERMS) NTH TERM (SEQUENCE) LOWER BOUND (NUMBER) n (Index of summation) Sigma Notation

  9. Definition: Anarithmetic seriesis a series associated with an arithmetic sequence. The sum of the first n terms: OR

  10. Examples: Find the sum of the first 100 natural numbers. 1 + 2 + 3 + 4 + … + 100

  11. Find the sum of the first 14 terms of the arithmetic series 2 + 5 + 8 + 11 + 14 + 17 +… Examples:

  12. Examples: Find the sum of the series

  13. 12.2 – Geometric Sequences and Series

  14. Arithmetic Series Geometric Series Sum of Terms Sum of Terms Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term

  15. Vocabulary of Sequences (Universal) ExplicitFormula Recursive Formula: an+1=an(r)

  16. Find the next three terms of 2, 3, 9/2, ___, ___, ___ 3 – 2 vs. 9/2 – 3… not arithmetic

  17. 1/2 x 9 NA 2/3

  18. The two geometric means are 6 and -18, since –2, 6, -18, 54 forms a geometric sequence Find two geometric means between –2 and 54 -2, ____, ____, 54 -2 54 4 NA x

  19. -3, ____, ____, ____

  20. x 9 NA

  21. x 5 NA

  22. *** Insert one geometric mean between ¼ and 4*** *** denotes trick question 1/4 3 NA

  23. 1/2 7 x

  24. Section 12.3 – Infinite Series

  25. Sequence Type Series 1, 4, 7, 10, 13, …. No Sum Infinite Arithmetic Finite Arithmetic 3, 7, 11, …, 51 Finite Geometric 1, 2, 4, …, 64 1, 2, 4, 8, … Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1

  26. Find the sum, if possible:

  27. Find the sum, if possible:

  28. Homework • Handout on Arithmetic and Geometric Sequences/Series—Due Tuesday for a grade

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