lucio
Uploaded by
25 SLIDES
428 VIEWS
250LIKES

What comes next?

DESCRIPTION

Dive into the world of arithmetic sequences with this comprehensive guide. Learn how to identify patterns in number sequences, find the next terms, and create expressions for nth terms. Explore examples featuring different sets of numbers, and practice by determining the next terms in various sequences. This tutorial simplifies the steps to analyze arithmetic sequences, making it easier for you to understand common differences, zero terms, and the construction of algebraic expressions. Perfect for students and anyone looking to strengthen their math skills!

1 / 25

Download Presentation

What comes next?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

Playing audio...

  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

More Related