GeoGebra-5.04/C3/Sequences-in-GeoGebra/English

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Visual Cue Narration
Slide Number 1

Title slide

Welcome to the Spoken Tutorial on Sequences in GeoGebra.
Slide Number 2

Learning Objectives

In this tutorial we will learn to,
  • Use spreadsheet view to create simple sequences
  • Use commands to create sequences and progressions
  • Divide the line segment into parts
  • Use Sequence command along with other commands
Slide Number 3

System Requirement

To record this tutorial, I am using;
  • Ubuntu Linux OS version 16.04
  • GeoGebra version 5.0438.0-d
Slide Number 4

Pre-requisites

https://spoken-tutorial.org

To follow this tutorial, learner should be familiar with GeoGebra interface.

For the prerequisite GeoGebra tutorials, please visit this website.

Show the list of commands. The commands used in the tutorial are provided in the Code Files link.
Cursor on GeoGebra interface. I have already opened GeoGebra interface.
Point to Algebra and Graphics views. We will first resize and place the Algebra view above the Graphics view.
Place the cursor on Algebra view's title bar. Place the cursor on the Algebra view's title bar.
Click and drag the mouse.

Point to the rectangular outline.

Release the mouse.

Click and drag the mouse.

When you see a rectangular outline, release the mouse.

Drag the boundary. Drag boundary to see the Graphics view clearly.
Cursor on GeoGebra interface. To create sequences, I will open the Spreadsheet view.
Click on View menu >> click on Spreasheet check-box Click on View menu and select Spreasheet check-box.
Cursor on the Spreadsheet view. Spreadsheet view opens next to the views.
Drag boundary of the Spreadsheet view. Drag the boundary to see the Spreadsheet view clearly.
Type 2 in cell A1 >> press Enter. In the cell A1 type 2 and press Enter.
Type A1+2 >> press Enter.

Point to cell A2.

In the cell A2 type A1+2 and press Enter.

Four is displayed in the cell A2.

Cursor in cell A2. Now we will create a sequence of numbers using the formula entered in cell A2.
Place cursor at the corner of cell A2 drag the fill handle.

Point to the sequence of even numbers.

Place the cursor at the corner of cell A2 and drag the fill handle till cell A15.

Observe that, a sequence of even numbers is displayed in the cells.

Cursor in Spreadsheet view. Now we will create a list for this sequence.
Select the cells from A1 to A15 by dragging.

Right-click to open the context menu.

Select the cells from A1 to A15 by dragging.

When we right-click on the selected cells, a context menu opens.

Select Create >> List.

Point to the list l1 in the Algebra view.

In the menu select Create and then List.

A list l1 is created in the Algebra view.

Drag boundary of the Algebra view. Drag the boundary of the Algebra view to see the complete list.
Point to the numbers in the list l1. l1 contains a list of even numbers from 2 to 30.
Click on Close button. Close the Spreadsheet view by clicking on the Close button.
Right-click on l1 in Algebra view. We will rename l1 as Evens.

In the Algebra view right-click on l1.

From the sub-menu, select Rename. From the sub-menu, select Rename.
In the Rename text box, type Evens >> click OK button. In the Rename text box, type Evens and click on the OK button.
Cursor on the interface. We can create a similar sequence for odd numbers using the Sequence command.
Type, Odds=Sequence.

Point to various options of Sequence command.

In the Input bar type Odds=Sequence.

Various options appear.

Select the option Sequence(<Expression>, <Variable>, <Start Value>, <End Value>).

Type Expression as 2n+1

Press Tab key.

Type Variable as n,

Press Tab key >> type Start Value as 0.

Press Tab key >> type End Value as 15.

Press Enter.

Type the Expression as 2n+1.

To go to the next argument, press Tab key.

Type Variable as n.

Press Tab key and type Start Value as 0.

Again press Tab key and type End Value as 15.

And then press Enter.

Point to the Odds sequence. Observe the sequence of odd numbers from 1 to 31 in the Algebra view.
Cursor on the interface. We will use the Sequence command to show a series of points in the Graphics view.
L_1=sequence[(n,0),n, 1,10]

Highlight the command in the input bar.

In the Input bar type the following command.

This command draws points at (n,0) where n goes from 1 to 10.

Press Enter.

Drag the Graphics view. Drag the Graphics view if you cannot see the points on the x-axis.
Cursor on the x-axis.

Point to the coordinates in the Algebra view.

We see a series of points on the x-axis from 1 to 10.

Coordinates of the points are shown in the Algebra view.

Move the cursor on the points. Let us change the position of these points.
In Algebra view double click on the list L1.

Point to the dialog box.

In the Algebra view double-click on the list L1.

The Redefine text box appears.

Type (0,n) in place of (n,0) >> click on OK button.

Cursor on the points.

Highlight the points in list L1.

In the box change n comma zero((n,0)) to zero comma n((0,n)) and click on the OK button.


Observe that the points move to y-axis.

Note the changes in the list L1.

Click on Zoom Out tool >> Click in Graphics view to zoom out. Using Zoom Out tool, click in Graphics view to see all the points on the y-axis.
Double click on list L1 in the Algebra view.

Type (n,n) in place of (0,n)>> click on OK button.

Again double-click on the list L1 in the Algebra view.


In the Redefine text box, change zero comma n((0,n)) to n comma n((n,n)) and click on the OK button.

Cursor on the points.


Highlight the points in list L1

Observe that the coordinates of the points change to n comma n((n,n)).

Note the changes in the list L1.

Cursor on the interface.
  • We will now a draw line segment to join zero comma zero((0,0)) and n comma n((n,n))
  • where n goes from 0 to 10 in the increments of 1.

For this we will use the Segment command along with the Sequence command.

Sequence[Segment((0, 0), (n, n)), n, 0, 10, 1] In the Input bar, type the following command and press Enter.
Point to the lines. Observe that a line is drawn to join the points.

A new list l1 is generated in the Algebra view.

Slide Number 5

Assignment

As as assignment:

Use the Sequence command to show a list of squares of numbers from 1 to 10.

Cursor on the interface. We will create arithmetic progression (AP) and geometric progression (GP) using the Sequence command.
Scroll and show the Additional material. For more information on AP and GP, please see the Additional Material provided along with this tutorial.
Click on File >> New Window. I will open a new GeoGebra window.
AP=Sequence[a+(n-1)d, n,0,10]

Press Enter.

In the Input bar, type the following command and press Enter.
Point to the dialog box.

Click on Create Sliders button.

Create Sliders dialog box appears.

Click on Create Sliders button.

Point to the sliders in the Graphics view. Number sliders a, n and d are created in the Graphics view.
Point to the sequence AP in the Algebra view. Observe that a new sequence AP is generated in the Algebra view.
Drag the boundary of the Algebra view. Drag the boundary to see the Algebra view clearly.
Point to the list AP,

[a+(n-1)d].

This command has generated a series of numbers a plus n minus 1 into d .

Here n goes from 0 to 10 and a and d go from -5 to 5.

Drag the sliders a and d.

Point to the sequence AP.

Drag the sliders a and d.

As we drag the sliders, observe the changes in the sequence AP.

Point to the sequence AP >> Graphics view. Notice that, sequence AP does have not any representation in the Graphics view.
Type in the input bar, Sequence[(n, a + d n), n, 0, 10] >> press Enter. In the Input bar, type in the following command and press Enter.
Observe the points in the Graphics view >> Algebra view. Observe that a list of points l1 is generated for the sequence AP.
Click on the Zoom Out tool >> click in the Graphics view. Click on the Zoom Out tool and click in the Graphics view to see all the points.
Cursor on the interface. Let us find the sum of n terms of the series.
Sum=n/2{2a+(n-1)d} >> Press Enter.

Point to the Algebra view.

In the Input bar, type the following command and press Enter.

Sum of n terms is displayed in the Algebra view.

Type a+d >> press Enter.

Point to f(x) in the Algebra view.

Now type a plus d x (a+dx) and press Enter.

A line f of x is drawn to join the points of the sequence AP.

Drag sliders a and d. Again, drag sliders a and d to see the changes.
Cursor in GeoGebra interface. Now we will generate a geometric progression.
Press Ctrl + A to select all objects.

Press Delete key on the key board.

Let us delete all the objects from the views.
GP=Sequence[(b r ^ n), n, 0, 10] In the Input bar type, the following command and press Enter.
Point to the dialog box.

Click on Create Sliders button.

Create Sliders dialog box appears.

Click on Create Sliders button.

Point to the sliders in the Graphics view. Sliders b, r and n are created in the Graphics view.
Drag boundary of the Algebra view. Drag the boundary to see the Algebra view clearly.
Point to the sequence in the Algebra view. A new sequence GP is created in the Algebra view.

This sequence generates a geometric progression of numbers from 0 to 10.

Here b and r go from -5 to 5.

Drag the sliders b and r. Drag the sliders b and r to see the changes in the geometric progression.
GP=Sequence[(n,b r ^ n), n, 0, 10]

Move the cursor on the points.

Type the following Sequence command and press Enter.

A series of points from 1 to 10 are plotted in the first quadrant.

Type b r ^ x >> press Enter. Now type b r raised to the power of x (b r ^ x) and press Enter.

Observe that a line is drawn to join the points.

Drag the sliders b and r.

Point to the curve g(x).

Drag the sliders b and r to see the changes in the curve and points on the curve.

We see a plot of an exponential function g of x.

Slide Number 6

Assignment.

As an assignment:

Find the sum of n terms in a geometric progression.

Cursor on the interface. Now we will divide a line segment into parts using the Sequence command.
Click on File >> New Window. I have opened a new GeoGebra window.
Click on Segment with Given Length tool >> click in Graphics view.

Point to the text box.

Under Line, click on Segment with Given Length tool.

And then click in Graphics view.


Segment with Given Length text box opens.

In the Length text box >> type 10 >> click OK. In the Length text box, type 10 and click OK.
Click on Slider tool >> click in the Graphics view. Now we will create a number slider n.

Click on Slider tool and click in the Graphics view.

Type Name as n

Type Min as 1, Max as 10, Increment as 1.

Click OK button.

In the Slider dialog box, type Name as n.

Change Min to 1, Max to 10 and Increment as 1.

Then click on OK button in the box.

sequence[A+(B-A)/n*k, k,1,n-1] In the Input bar type the following command.
Point to the command.

Press Enter.

Using this command we are generating a series of points on the segment AB.

Here k goes from 1 to n-1.

Observe that k is expressed in terms of n, so we do not need a slider for k.

Press Enter.

Drag the slider n to see the partitions. Drag the slider n and see the partitions in the segment AB.
Ctrl + A to select all objects.

Press Delete key on the key board.

Let us delete all the objects from the views.
Cursor on the interface. We can use the Sequence command along with additional commands.
Sequence[Circle[(0,0) , r ], r , 0 , 5 , 0.25] For example, type the following command and press Enter.

Using this command we have drawn concentric circles with origin at zero comma zero((0,0)) and radius r.

Here r goes from 0 to 5 in the increments of 0.25.

Point to l1.

In the Algebra view right-click on L1 >> select Delete.

Let us delete l1.

In the Algebra view right-click on l1 and select Delete.

Sequence[x^2 + c x, c, -5, 5, 0.5] Next type this command and press Enter.

Using this command we have drawn a family of parabolas x^2+cx.

Here c goes from -5 to 5 in the increments of 0.5.

Slide Number 7

Assignment

Generate a sequence to draw:

  • Polygons at (0,0) and (1,0) of n sides, where n goes from 3 to 10.

Hint: type [Polygon[(point), (point), n], n, start value of n, end value of n]

As an assignment:

Generate a sequence to draw polygons.

Slide Number 8

Assignment


Generate sequences to draw:

  • Parabolas x^2+c where c goes from -5 to 5 in increments of 0.5
  • Parabolas c x^2+ 2c x-1, where c goes from -5 to 5 in increments of 0.5
And generate sequences to draw parabolas.
Let us summarize
Slide Number 9

Summary

In this tutorial we have learnt to,
  • Use spreadsheet view to create simple sequences
  • Use commands to create sequences and progressions
  • Divide the line segment into parts
  • Use sequence command along with other commands
Slide Number 10

About Spoken Tutorial project

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

Slide Number 11

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  • gives certificates.

For more details, please write to us.

Slide Number 12

Forum for specific questions:

  • Do you have questions in THIS Spoken Tutorial?
  • Please visit this site
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  • Explain your question briefly
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Please post your timed queries on this forum.
Slide Number 13

Acknowledgement

Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.

Contributors and Content Editors

Madhurig, Nancyvarkey, PoojaMoolya

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