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

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Time Narration
00:01 Welcome to the Spoken Tutorial on Sequences in GeoGebra.
00:06 In this tutorial we will learn to, Use spreadsheet view to create simple sequences
00:13 Use commands to create sequences and progressions
00:18 Divide the line segment into parts
00:21 Use Sequence command along with other commands
00:25 To record this tutorial, I am using;

Ubuntu Linux OS version 16.04

00:33 GeoGebra version 5.0438.0-d
00:39 To follow this tutorial, learner should be familiar with GeoGebra interface.
00:46 For the prerequisite GeoGebra tutorials, please visit this website.
00:51 The commands used in the tutorial are provided in the Code Files link.
00:57 I have already opened GeoGebra interface.
01:01 We will first resize and place the Algebra view above the Graphics view.
01:07 Place the cursor on the Algebra views' title bar.
01:11 Click and drag the mouse.
01:14 When you see a rectangular outline, release the mouse.
01:19 Drag boundary to see the Graphics view clearly.
01:23 To create sequences, I will open the Spreadsheet view.
01:27 Click on View menu and select Spreasheet check-box.
01:32 Spreadsheet view opens next to the views.
01:36 Drag the boundary to see the Spreadsheet view clearly.
01:40 In the cell A1 type 2 and press Enter.
01:45 In the cell A2 type A1+2 and press Enter.

Four is displayed in the cell A2.

01:53 Now we will create a sequence of numbers using the formula entered in cell A2.
01:59 Place the cursor at the corner of cell A2 and drag the fill handle till cell A15.
02:07 Observe that, a sequence of even numbers is displayed in the cells.
02:12 Now we will create a list for this sequence.
02:16 Select the cells from A1 to A15 by dragging.
02:20 When we right-click on the selected cells, a context menu opens.
02:25 In the menu select Create and then List.
02:30 A list l1 is created in the Algebra view.
02:34 Drag the boundary of the Algebra view to see the complete list.
02:39 l1 contains a list of even numbers from 2 to 30.
02:44 Close the Spreadsheet view by clicking on the Close button.
02:48 We will rename l1 as Evens. In the Algebra view right-click on l1.
02:56 From the sub-menu, select Rename.
02:59 In the Rename text box, type Evens and click on the OK button.
03:06 We can create a similar sequence for odd numbers using the Sequence command.
03:12 In the Input bar type Odds=Sequence.

Various options appear.

03:20 Select the option Sequence(<Expression>, <Variable>, <Start Value>, <End Value>).
03:27 Type the Expression as 2n+1.
03:30 To go to the next argument, press Tab key.

Type Variable as n.

03:37 Press Tab key and type Start Value as 0.
03:41 Again press Tab key and type the End Value as 15.

And then press Enter.

03:48 Observe the sequence of odd numbers from 1 to 31 in the Algebra view.
03:54 We will use the Sequence command to show a series of points in the Graphics view.
03:59 In the Input bar type the following command.
04:03 This command draws points at (n,0) where n goes from 1 to 10.

Press Enter.

04:11 Drag the Graphics view if you cannot see the points on the x-axis.
04:16 We see a series of points on the x-axis from 1 to 10.
04:21 Coordinates of the points are shown in the Algebra view.
04:25 Let us change the position of these points.
04:28 In the Algebra view double-click on the list L1.
04:32 The Redefine text box appears.
04:35 In the box change n comma zero to zero comma n and click on the OK button.
04:43 Observe that the points move to y-axis.
04:46 Note the changes in the list L1.
04:49 Using Zoom Out tool, click in the Graphics view to see all the points on the y-axis.
04:45 Again double-click on the list L1 in the Algebra view.
04:59 In the Redefine text box, change zero comma n to n comma n and click on the OK button.
05:08 Observe that the coordinates of the points change to n comma n.
05:13 Note the changes in the list L1.
05:16 We will now a draw line segment to join zero comma zero and n comma n
where n goes from 0 to 10 in the increments of 1. 
05:28 For this we will use the Segment command along with the Sequence command.
05:33 In the Input bar, type the following command and press Enter.
05:38 Observe that a line is drawn to join the points.
05:42 A new list l1 is generated in the Algebra view.
05:47 As as assignment:

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

05:56 We will create arithmetic progression (AP) and geometric progression (GP) using the Sequence command.
06:03 For more information on AP and GP, please see the Additional Material provided along with this tutorial.
06:11 I will open a new GeoGebra window.
06:15 In the Input bar, type the following command and press Enter.
06:20 Create Sliders dialog box appears.
06:24 Click on Create Sliders button.
06:27 Number sliders a, n and d are created in the Graphics view.
06:33 Observe that a new sequence AP is generated in the Algebra view.
06:38 Drag the boundary to see the Algebra view clearly.
06:42 This command has generated a series of numbers a plus n minus 1 into d .
06:48 Here a and d go from -5 to 5.
06:53 Drag the sliders a and d.
06:56 As we drag the sliders, observe the changes in the sequence AP.
07:01 Notice that, sequence AP does have not any representation in the Graphics view.
07:07 In the Input bar, type the following command and press Enter.
07:13 Observe that a list of points l1 is generated for the sequence AP.
07:18 Click on the Zoom Out tool and click in the Graphics view to see all the points.
07:25 Let us find the sum of n terms of the series.
07:29 In the Input bar, type the following command and press Enter.
07:34 Sum of n terms is displayed in the Algebra view.
07:38 Now type a plus d x and press Enter.
07:43 A line f of x is drawn to join the points of the sequence AP.
07:48 Again, drag sliders a and d to see the changes.
07:54 Now we will generate a geometric progression.
07:57 Let us delete all the objects from the views.
08:01 In the Input bar type, the following command and press Enter.
08:07 Create Sliders dialog box appears.
08:11 Click on Create Sliders button.
08:14 Sliders b, r and n are created in the Graphics view.
08:19 Drag the boundary to see the Algebra view clearly.
08:23 A new sequence GP is created in the Algebra view.
08:27 This sequence generates a geometric progression of numbers from 0 to 10.

Here b and r go from -5 to 5.

08:38 Drag the sliders b and r to see the changes in the geometric progression.
08:45 Type the following Sequence command and press Enter.
08:50 A series of points from 0 to 10 are plotted in the first quadrant.
08:55 Now type b r raised to the power of x and press Enter.
09:01 Observe that a line is drawn to join the points.
09:05 Drag the sliders b and r to see the changes in the curve and points on the curve.
09:11 We see a plot of an exponential function g of x.
09:16 As an assignment:

Find the sum of n terms in a geometric progression.

09:23 Now we will divide a line segment into parts using the Sequence command.
09:28 I have opened a new GeoGebra window.
09:31 Under Line, click on Segment with Given Length tool.

And then click in Graphics view.

09:38 Segment with Given Length text box opens.
09:42 In the Length text box, type 10 and click OK.
09:47 Now we will create a number slider n.
09:50 Click on Slider tool and click in the Graphics view.
09:56 In the Slider dialog box, type Name as n.
10:00 Change Min to 1, Max to 10 and Increment as 1.
10:07 Then click on OK button in the box.
10:11 In the Input bar type the following command.
10:15 Using this command we are generating a series of points on the segment AB.
10:21 Here k goes from 1 to n-1.
10:25 Observe that k is expressed in terms of n, so we do not need a slider for k.

Press Enter.

10:34 Drag the slider n and see the partitions in the segment AB.
10:42 Let us delete all the objects from the views.
10:46 We can use the Sequence command along with additional commands.
10:51 For example, type the following command and press Enter.
10:57 Using this command we have drawn concentric circles with origin at zero comma zero and radius r.
11:05 Here r goes from 0 to 5 in the increments of 0.25.
11:11 Let us delete l1.

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

11:19 Next type this command and press Enter.
11:23 Using this command we have drawn a family of parabolas x square + cx.

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

11:36 As an assignment:

Generate a sequence to draw polygons.

11:42 And generate sequences to draw parabolas.
11:47 Let us summarize
11:49 In this tutorial we have learnt to, Use spreadsheet view to create simple sequences
11:56 Use commands to create sequences and progressions

Divide the line segment into parts

12:03 Use sequence command along with other commands
12:07 The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

12:15 The Spoken Tutorial Project ' team:

Conducts workshops and gives certificates.

12:20 For more details, please write to us.
12:23 Please post your timed queries on this forum.
12:27 Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.
12:33 More information on this mission is available at this link.
12:38 This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.

Contributors and Content Editors

PoojaMoolya