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

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.

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