GeoGebra-5.04/C3/Sequences-in-GeoGebra/English-timed
From Script | Spoken-Tutorial
| 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 5.0.438.0-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. |
| 04:55 | 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. |
