Using Technology to Work with Sequences: IM Alg2.1.4
[url=https://im.kendallhunt.com/HS/teachers/3/1/4/preparation.html]“Using Technology to Work with Sequences”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.1.4 Lesson
- IM Alg2.1.4 Lesson: Using Technology to Work with Sequences
- Alg2.1.4 Practice
- IM Alg2.1.4 Practice: Using Technology to Work with Sequences
IM Alg2.1.4 Lesson: Using Technology to Work with Sequences
Here you have a blank spreadsheet.
Type the following in each cell:
[size=150][table][tr][td]In A1, type 2[/td][td]In B1, type =A1+A2[/td][/tr][tr][td]In A2, type 3[/td][td]In B2, type =A3*A4[/td][/tr][tr][td]In A3, type -10[/td][td]In B3, type =B1+333[/td][/tr][tr][td]In A4, type 1/5[/td][td]In B4, type =abs(B2)[/td][/tr][/table][/size][br]Look at the numbers that appear in B1, B2, B3, and B4 after you press enter. Where did these numbers come from?[br]
Experiment with typing some different values in A1, A2, A3, and A4. Describe what happens.[br]
[size=150]Experiment with typing some new formulas in some new cells.[br][br][/size]Can you figure out how to raise a number to a power?
What happens if you forget to start a formula with the = symbol?
Here you have another blank spreadsheet. In A1, type 10 and enter.
In A2, type =A1+3 and enter.[br][br]Click once on cell A2 to highlight it. See the little + in the lower-right corner? Click and drag it down to highlight several rows in that column and then let go. (This is known as “fill down.”) Describe what happens.[br]
What simple thing can you edit so that column A shows the sequence 12, 15, 18, . . .?
What simple things can you edit so that column A shows the sequence 12, 11, 10, . . .?
In B2, type =B1*0.5 and enter. [br][br]Click on cell B2 and fill down. Describe what happens.
What simple thing can you edit so that column B shows the sequence 10, 5, 2.5, . . .?
What simple things can you edit so that column B shows the sequence 10, 30, 90, . . .?
In column C, starting at C1 and going down, type these terms of a geometric sequence: 700, 70, 7, 0.7, 0.07.
In cell D2, type =C2/C1. What is the result?
What is the meaning of the result?
Click on cell D2 and fill down. What happens?
In column E, starting at E1 and going down, type these terms of an arithmetic sequence: 7, 10.5, 14, 17.5.
In cell F2, type =E2-E1. What is the result?
What is the meaning of the result?
Click on cell F2 and fill down. What happens?
Use the spreadsheet to decide whether the sequence 8, 12, 18, 27, 40.5 is arithmetic or geometric, and find its rate of change or growth factor.
Use the spreadsheet to decide whether the sequence 50, 42.1, 34.2, 26.3 is arithmetic or geometric, and find its rate of change or growth factor.
Here you have another blank spreadsheet.
In column A, starting in A1 and going down, enter the numbers 0 through 9. What could you type into B1 and then fill down to the 10th row that gives the first 10 terms of a linear function whose rate of change is 2 and vertical intercept is 5?
Follow your teacher’s instructions to create a new table with 2 columns. Learn how the 2 numbers in each row can be plotted as points in the coordinate plane.
[list][*]Change the numbers in the table so that all of the plotted points lie along a diagonal line with a positive slope.[br][/*][*]Change the numbers in the table so that all of the plotted points lie along a horizontal line.[br][/*][*]Change the numbers in the table so that the graph created does [i]not[/i] represent a function.[br][/*][/list]
Here you have a graphing utility.
Follow your teacher’s instructions to make one column a function of the other.
[list][*]Change the expression in the second column so that the plotted points lie on a line with a different steepness.[/*][*]Change the expression in the second column so that the plotted points do not lie on a line.[/*][*]Change the table so that some of the points are plotted in the second quadrant of the graph (the upper-left quadrant).[/*][/list]
IM Alg2.1.4 Practice: Using Technology to Work with Sequences
Here you have a blank spreadsheet. In A1, type 2 and enter.
What should you type into cell A2 to generate the sequence 2, 4, 8, 16, 32, . . . when you fill down the column?[br]
What should you type into cell A2 to generate the sequence 2, 4, 6, 8, 10, . . . when you fill down the column?[br]
Here you have another blank spreadsheet. In A1, type 400 and enter.
What should you type into cell A2 to generate the sequence 400, 200, 100, 50, 25, . . . when you fill down the column?[br]
What should you type into cell A2 to generate the sequence 400, 325, 250, 175, 100, . . . when you fill down the column?[br]
Here you have another blank spreadsheet.
If cell A1 = 5 and cell A2 = A1 * 3 + 2, what are the first 5 terms of the sequence?[br]
If cell A1 = 1 and cell A2 = (A1 + 2) * 3, what are the first 5 terms of the sequence?[br]
If cell A1 = 2 and cell A2 = (A1 + 2) * 3, what are the first 5 terms of the sequence?[br]
Here you have another blank spreadsheet.
Find the first 5 terms of a geometric sequence that starts with -5 and has a growth factor of -1.[br]
Find the first 5 terms of a geometric sequence that starts with -20 and has a growth factor of 0.5.[br]
Find the first 5 terms of an arithmetic sequence that starts with -20 and has an rate of change of 5.[br]
Find the first 5 terms of an arithmetic sequence that starts with 43 and has an rate of change of -7.[br]
Here is the graph of a sequence.
Explain how you know this sequence is arithmetic.[br]
Explain how you know this sequence is not geometric.[br]
The first two terms of a geometric sequence are 6 and 3.
Explain why there is only one geometric sequence with these first two terms.[br]
What are the next 3 terms of this geometric sequence?[br]