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What comes next?

What comes next?. Arithmetic Sequences. Algebraic Sequence. A pattern of numbers with a constant difference between terms. Examples: 1, 5, 9, 13, 17 -7, -1, 5, 11, 17 21, 20, 19, 18, 17. Write the next two terms in the sequence…. 7, 13, 19, 25, ___, ___. 31. 37.

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What comes next?

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  1. What comes next? Arithmetic Sequences

  2. Algebraic Sequence A pattern of numbers with a constant difference between terms. Examples: 1, 5, 9, 13, 17 -7, -1, 5, 11, 17 21, 20, 19, 18, 17

  3. Write the next two terms in the sequence….. 7, 13, 19, 25, ___, ___ 31 37

  4. Write the next two terms in the sequence….. 14, 22, 30, 38, 46, ___, ___ 54 62

  5. Write the next two terms in the sequence….. 3, 7, 11, 15, ___, ___ 19 23

  6. Write the next three terms in the sequence….. 4, 9, 14, 19, ___, ___, ___ 24 29 34

  7. Write the next four terms in the sequence….. 7, 12, 17, ___, ___, ___, ___ 22 27 32 37

  8. Write the first five terms of the sequence represented….. • Start at 3 and increase by 10 • Start at 4 and increase by 5 • Start at 6 and increase by 2 3, 13, 23, 33, 43 4, 9, 14, 19, 24 6, 8, 10, 12, 14

  9. EXAMPLE 1 Write an expression for the nth term in the sequence 3, 5, 7, 9, 11, …? Step 1:  Construct a process chart showing the position and the corresponding term. 3 5 9 11 7 +2 +2 +2 +2

  10. Determine the common difference (the change) of the terms. Step 2 Common Difference: 2 This is thecoefficientof n. 2n

  11. Reverse the pattern to find the “zero” term. Step 3 1 3 5 9 11 7 -2 Zero term: 1

  12. Common Difference: 2 Finishing it Off Zero Term: 1 2 1 n + 2n+ 1

  13. EXAMPLE 1 Write an expression for the nth term in the sequence 1, 4, 13, 16, 25, …? Step 1:  Construct a process chart showing the position and the corresponding term. 1 4 16 25 3 9 3 9

  14. Determine the common difference (the change) of the terms. Step 2 Common Difference: 3 This is thecoefficientof n. 3n

  15. Reverse the pattern to find the “zero” term. Step 3 -2 1 4 16 25 13 -3 Zero term: -2

  16. Common Difference: 3 Finishing it Off Zero Term: 2 2 3 n- 3n - 2

  17. Let’s review! Write the first five terms of the sequence represented….. • Start at 4 and increase by 3 n 4 7 10 13 16 1 2 3 4 5 Now let’s make a table…

  18. Write the first five terms of the sequence represented by….. 2n + 1 n 1 2 3 4 5 3 5 7 9 11 The nth term is the position in the sequence.

  19. Now it’s your turn… • Write the first five terms of the sequence represented by….. Hint: Make a Table!!! 3n + 2 5n – 1 n n 1 2 3 4 5 5 8 11 14 17 1 2 3 4 5 4 9 14 19 24

  20. Let’s analyze arithmetic sequences... How do we identify the nth term of each sequence? 7, 12, 17, 22, ….. The nth term is ANY position (number) in the sequence.

  21. 5 Let’s write an expression to identify the nth term 1. What is the common difference? 2. What is the zero term? 2 2 + - 5 5n + 2 +5 +5 +5

  22. Let’s write another expression… 7, 13, 19, 25, ….. 6 n 1 + - 6 1 2 3 4 7 13 19 25 +6 6n + 1 +6 +6

  23. Let’s try another one… 3, 7, 11, 15, ….. n Hint: Make a Table!!!

  24. Think / Write / Share: 1) What are the steps to continuing a sequence? 2) What are the steps to creating a table given an expression? 3) What are the steps to writing an expression to describe a sequence?

  25. Exit Poll • Which of the following tasks is most difficult for you? Why? • Finding the next two terms in a sequence • Using an expression to find terms in a sequence • Writing the Algebraic Expression for a sequence

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