Welcome to the Spoken Tutorial on Sequences in GeoGebra.
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
To record this tutorial, I am using; Ubuntu Linux OS version 16.04
GeoGebra version 5.0438.0-d
To follow this tutorial, learner should be familiar with GeoGebra interface.
For the prerequisite GeoGebra tutorials, please visit this website.
The commands used in the tutorial are provided in the Code Files link.
I have already opened GeoGebra interface.
We will first resize and place the Algebra view above the Graphics view.
Place the cursor on the Algebra views' title bar.
Click and drag the mouse.
When you see a rectangular outline, release the mouse.
Drag boundary to see the Graphics view clearly.
To create sequences, I will open the Spreadsheet view.
Click on View menu and select Spreasheet check-box.
Spreadsheet view opens next to the views.
Drag the boundary to see the Spreadsheet view clearly.
In the cell A1 type 2 and press Enter.
In the cell A2 type A1+2 and press Enter. Four is displayed in the cell A2.
Now we will create a sequence of numbers using the formula entered in cell A2.
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.
Now we will create a list for this sequence.
Select the cells from A1 to A15 by dragging.
When we right-click on the selected cells, a context menu opens.
In the menu select Create and then List.
A list l1 is created in the Algebra view.
Drag the boundary of the Algebra view to see the complete list.
l1 contains a list of even numbers from 2 to 30.
Close the Spreadsheet view by clicking on the Close button.
We will rename l1 as Evens. In the Algebra view right-click on l1.
From the sub-menu, select Rename.
In the Rename text box, type Evens and click on the OK button.
We can create a similar sequence for odd numbers using the Sequence command.
In the Input bar type Odds=Sequence. Various options appear.
Select the option Sequence(, , , ).
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 the End Value as 15. And then press Enter.
Observe the sequence of odd numbers from 1 to 31 in the Algebra view.
We will use the Sequence command to show a series of points in the Graphics view.
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 if you cannot see the points on the x-axis.
We see a series of points on the x-axis from 1 to 10.
Coordinates of the points are shown in the Algebra view.
Let us change the position of these points.
In the Algebra view double-click on the list L1.
The Redefine text box appears.
In the box change n comma zero to zero comma n and click on the OK button.
Observe that the points move to y-axis.
Note the changes in the list L1.
Using Zoom Out tool, click in the Graphics view to see all the points on the y-axis.
Again double-click on the list L1 in the Algebra view.
In the Redefine text box, change zero comma n to n comma n and click on the OK button.
Observe that the coordinates of the points change to n comma n.
Note the changes in the list L1.
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.
For this we will use the Segment command along with the Sequence command.
In the Input bar, type the following command and press Enter.
Observe that a line is drawn to join the points.
A new list l1 is generated in the Algebra view.
As as assignment: Use the Sequence command to show a list of squares of numbers from 1 to 10.
We will create arithmetic progression (AP) and geometric progression (GP) using the Sequence command.
For more information on AP and GP, please see the Additional Material provided along with this tutorial.
I will open a new GeoGebra window.
In the Input bar, type the following command and press Enter.
Create Sliders dialog box appears.
Click on Create Sliders button.
Number sliders a, n and d are created in the Graphics view.
Observe that a new sequence AP is generated in the Algebra view.
Drag the boundary to see the Algebra view clearly.
This command has generated a series of numbers a plus n minus 1 into d .
Here a and d go from -5 to 5.
Drag the sliders a and d.
As we drag the sliders, observe the changes in the sequence AP.
Notice that, sequence AP does have not any representation in the Graphics view.
In the Input bar, type the following command and press Enter.
Observe that a list of points l1 is generated for the sequence AP.
Click on the Zoom Out tool and click in the Graphics view to see all the points.
Let us find the sum of n terms of the series.
In the Input bar, type the following command and press Enter.
Sum of n terms is displayed in the Algebra view.
Now type a plus d x and press Enter.
A line f of x is drawn to join the points of the sequence AP.
Again, drag sliders a and d to see the changes.
Now we will generate a geometric progression.
Let us delete all the objects from the views.
In the Input bar type, the following command and press Enter.
Create Sliders dialog box appears.
Click on Create Sliders button.
Sliders b, r and n are created in the Graphics view.
Drag the boundary to see the Algebra view clearly.
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 to see the changes in the geometric progression.
Type the following Sequence command and press Enter.
A series of points from 0 to 10 are plotted in the first quadrant.
Now type b r raised to the power of x and press Enter.
Observe that a line is drawn to join the points.
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.
As an assignment: Find the sum of n terms in a geometric progression.
Now we will divide a line segment into parts using the Sequence command.
I have opened a new GeoGebra window.
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 and click OK.
Now we will create a number slider n.
Click on Slider tool and click in the Graphics view.
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.
In the Input bar type the following command.
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 and see the partitions in the segment AB.
Let us delete all the objects from the views.
We can use the Sequence command along with additional commands.
For example, type the following command and press Enter.
Using this command we have drawn concentric circles with origin at zero comma zero and radius r.
Here r goes from 0 to 5 in the increments of 0.25.
Let us delete l1. In the Algebra view right-click on l1 and select Delete.
Next type this command and press Enter.
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.
As an assignment: Generate a sequence to draw polygons.
And generate sequences to draw parabolas.
Let us summarize
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
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