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4.7: Arithmetic sequences

4.7: Arithmetic sequences. I can write a recursive formulas given a sequence. Day 1. Describe a pattern in each sequence. Then find the next two terms. 22. 7, 10, 13, 16 ___, ___, …. 19. Add 3. 48. 3, 6, 12, ___, ___, …. 24. Mult by 2. 66. 99, 88, 77, ___, ___, …. 55.

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4.7: Arithmetic sequences

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  1. 4.7: Arithmetic sequences I can write a recursive formulas given a sequence. Day 1

  2. Describe a pattern in each sequence. Then find the next two terms. 22 7, 10, 13, 16 ___, ___, … 19 Add 3 48 3, 6, 12, ___, ___, … 24 Mult by 2 66 99, 88, 77, ___, ___, … 55 Subtract 11

  3. Arithmetic sequences: In an arithmetic sequence: The difference between each consecutive term is constant. This difference is called the common difference (d). Ex: 3, 5, 7, 9, … 2 Common difference for the above sequence:

  4. If there is a common difference, what is it? Common difference: 22 7, 10, 13, 16 ___, ___, … 19 3 48 Common difference: 3, 6, 12, ___, ___, … 24 There isn’t one. 66 99, 88, 77, ___, ___, … 55 Common difference: -11

  5. Is the following sequence arithmetic? If it is, describe the pattern. a. 5, 10, 20, 40, … no Why not: I started with 5 and then multiplied by 2 each time. b. 5, 8, 11, 14… I started with 5 and then added 3 each time. yes c. 20, 5, -10, -25, … I started with 20 and then added -15 each time. yes

  6. An ordered list of numbers defined by a starting value (number) and a rule to find the general term. Recursive Formula: first term A(1)= A(n)= General term or nth term A(n-1)= Previous term Given the following recursive formula, find the first 4 terms. 20 A(1)= 20, 26, 32, 38 A(n)= A(n-1) + 6 1st term2nd term3rd term 4th term Think: previous term + 6 Given the following recursive formula, find the first 4 terms. A(1)= -18 -18, -21, -24, -27, 1st term2nd term3rd term 4th term A(n-1) - 3 A(n)= Think: previous term -3

  7. Write a recursive formula for each sequence. 7 7, 10, 13, 16, … Recursive rule: 7 A(1)= A(1)= 7 A(n) = A(n-1) + 3 A(1)= ____ +3 A(n)= A(n-1) A(n)= A(n-1) + d 97, 87, 77, 67 … 3 3, 9,15, 21,… 3 A(1)= 3 A(n) = A(n-1) + 6 A(1)= 97 A(1)= + 6 A(n)= A(n-1) A(n)= A(n-1) - 10 Homework: pg 279: 9-35

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