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Ch. 11 – Sequences & Series

Ch. 11 – Sequences & Series. 11.1 – Sequences as Functions. Arithmetic sequence -. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d.

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Ch. 11 – Sequences & Series

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  1. Ch. 11 – Sequences & Series 11.1 – Sequences as Functions

  2. Arithmetic sequence -

  3. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d

  4. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, …

  5. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36

  6. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 + 6

  7. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 + 6

  8. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 + 6 + 6

  9. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 + 6 + 6

  10. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 + 6 + 6 + 6

  11. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 + 6 + 6 + 6

  12. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 + 6 + 6 + 6 + 6

  13. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 60 + 6 + 6 + 6 + 6

  14. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 60 + 6 + 6 + 6 + 6 + 6

  15. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 60 66 + 6 + 6 + 6 + 6 + 6

  16. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 60 66 + 6 + 6 + 6 + 6 + 6 + 6

  17. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 60 66 72 + 6 + 6 + 6 + 6 + 6 + 6

  18. Arithmetic sequence – a sequence of numbers in which each term after the first is found by adding or subtracting a constant number, called the “common difference” d Ex. 1 Find the next four terms. a) 36, 42, 48, … 36 42 48 54 60 6672 + 6 + 6 + 6 + 6 + 6 + 6

  19. b) 23, 18, 13, …

  20. b) 23, 18, 13, … 23

  21. b) 23, 18, 13, … 23 - 5

  22. b) 23, 18, 13, … 23 18 - 5

  23. b) 23, 18, 13, … 23 18 - 5 - 5

  24. b) 23, 18, 13, … 23 18 13 - 5 - 5

  25. b) 23, 18, 13, … 23 18 13 - 5 - 5 - 5

  26. b) 23, 18, 13, … 23 18 13 8 - 5 - 5 - 5

  27. b) 23, 18, 13, … 23 18 13 8 3 -2 -7 - 5 - 5 - 5 - 5 - 5 - 5

  28. Geometric sequence

  29. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r

  30. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, ___

  31. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, ___ 24 8

  32. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, ___ ·3

  33. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, ___ ·3 72 24

  34. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, ___ ·3 ·3

  35. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 72·3 ·3 ·3

  36. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 216 ·3 ·3

  37. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 216 ·3 ·3 b) 270, 90, 30,

  38. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 216 ·3 ·3 b) 270, 90, 30, ÷3

  39. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 216 ·3 ·3 b) 270, 90, 30, ·⅓

  40. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 216 ·3 ·3 b) 270, 90, 30, ·⅓ ·⅓

  41. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 216 ·3 ·3 b) 270, 90, 30, 30·⅓ ·⅓ ·⅓

  42. Geometric sequence – a sequence of numbers in which each term after the first is found by multiplying the previous terms by a constant number, called the “common ratio” r Ex. 2 Find the next term. a) 8, 24, 72, 216 ·3 ·3 b) 270, 90, 30, 10 ·⅓ ·⅓

  43. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 …

  44. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 … 24-16=8

  45. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 … 24-16=8, 36-24=12

  46. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 … 24-16=8, 36-24=12NOT ARITHMETIC

  47. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 … 24-16=8, 36-24=12NOT ARITHMETIC 24= 1.5 16

  48. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 … 24-16=8, 36-24=12NOT ARITHMETIC 24= 1.5, 36= 1.5 16 24

  49. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 … 24-16=8, 36-24=12NOT ARITHMETIC 24=1.5, 36=1.5 GEOMETRIC 16 24

  50. Ex. 3 Determine whether each sequence is arithmetic, geometric, or neither. Then graph each sequence. a) 16, 24, 36, 54 … 24-16=8, 36-24=12NOT ARITHMETIC 24=1.5, 36=1.5 GEOMETRIC 16 24

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