PoojaMoolya at 09:25, 30 January 2020

2020-01-30T09:25:09Z

PoojaMoolya at 09:12, 10 October 2019

2019-10-10T09:12:46Z

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 || Welcome to the Spoken Tutorial on '''Sequences in GeoGebra'''. |- ||00:06 || In this tutorial we will learn to,..."

2019-09-27T09:49:01Z

Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 || Welcome to the Spoken Tutorial on '''Sequences in GeoGebra'''. |- ||00:06 || In this tutorial we will learn to,..."

New page

{|border=1
||'''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.

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||01:14
||When you see a rectangular outline, release the mouse.

|-
|| 01:19
|| Drag boundary to see the '''Graphics view''' clearly.

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|| 01:23
|| To create sequences, I will open the '''Spreadsheet view'''.

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|| 01:27
|| Click on '''View''' menu and select '''Spreasheet''' check-box.

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|| 01:32
|| '''Spreadsheet view''' opens next to the '''views'''.

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|| 01:36
|| Drag the boundary to see the '''Spreadsheet view''' clearly.

|-
|| 01:40
|| In the cell '''A1''' type 2 and press '''Enter'''.

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|| 01:45
|| In the cell '''A2''' type '''A1+2''' and press '''Enter'''.

Four is displayed in the cell '''A2'''.

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|| 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.

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|| 02:12
|| Now we will create a list for this sequence.

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|| 02:16
|| Select the cells from '''A1''' to '''A15''' by dragging.

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|| 02:20
||When we right-click on the selected cells, a context menu opens.

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|| 02:25
|| In the menu select '''Create''' and then '''List'''.

|-
||02:30
||A list '''l1''' is created in the '''Algebra view'''.

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|| 02:34
|| Drag the boundary of the '''Algebra view''' to see the complete list.

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|| 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.

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|| 02:48
|| We will rename '''l1''' as '''Evens'''. In the '''Algebra view''' right-click on '''l1'''.

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|| 02:56
|| From the sub-menu, select '''Rename'''.

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|| 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'''.

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|| 03:12
|| In the '''Input bar''' type '''Odds=Sequence'''.

Various options appear.

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|| 03:20
||Select the option '''Sequence(<Expression>, <Variable>, <Start Value>, <End Value>)'''.

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|| 03:27
|| Type the '''Expression''' as '''2n+1'''.

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||03:30
||To go to the next '''argument''', press '''Tab''' key.

Type '''Variable''' as '''n'''.

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||03:37
||Press '''Tab''' key and type '''Start Value''' as 0.

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||03:41
|| Again press '''Tab''' key and type the '''End Value''' as 15.

And then press '''Enter'''.

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||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'''.

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|| 03:59
|| In the '''Input bar''' type the following '''command'''.

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||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.

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||04:21
|| Coordinates of the points are shown in the '''Algebra view'''.

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|| 04:25
|| Let us change the position of these points.

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|| 04:28
|| In the '''Algebra view '''double-click on the list '''L1'''.

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||04:32
|| The '''Redefine''' text box appears.

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|| 04:35
|| In the box change n comma zero to zero comma n and click on the '''OK''' button.

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||04:43
|| Observe that the points move to y-axis.

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||04:46
||Note the changes in the list '''L1'''.

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|| 04:49
|| Using '''Zoom Out''' tool, click in the '''Graphics view''' to see all the points on the y-axis.

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|| 04:45
|| Again double-click on the list '''L1''' in the '''Algebra view'''.

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||04:59
|| In the '''Redefine''' text box, change zero comma n to n comma n and click on the '''OK''' button.

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|| 05:08
|| Observe that the coordinates of the points change to n comma n.

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||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.

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||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.

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||05:42
|| A new list '''l1''' is generated in the '''Algebra view'''.

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|| 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'''.

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|| 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.

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||06:24
|| Click on '''Create Sliders''' button.

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|| 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.

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|| 06:42
|| This '''command''' has generated a series of numbers '''a plus n minus 1 into d''' .

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||06:48
|| Here '''a''' and '''d''' go from -5 to 5.

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|| 06:53
|| Drag the '''sliders a''' and '''d'''.

|-
||06:56
|| As we drag the sliders, observe the changes in the sequence '''AP'''.

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|| 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'''.

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|| 07:13
|| Observe that a list of points '''l1''' is generated for the sequence '''AP'''.

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|| 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'''.

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|| 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.

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|| 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.

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|| 09:42
|| In the '''Length''' text box, type 10 and click '''OK'''.

|-
|| 09:47
|| Now we will create a number '''slider n'''.

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||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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-|| '''GeoGebra''' version 5.0438.0-d
+|| '''GeoGebra''' version 5.0.438.0-d
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 |-
-|| 04:45
+|| 04:55
 || Again double-click on the list '''L1''' in the '''Algebra view'''.

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

PoojaMoolya at 09:25, 30 January 2020

PoojaMoolya at 09:12, 10 October 2019

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 || Welcome to the Spoken Tutorial on '''Sequences in GeoGebra'''. |- ||00:06 || In this tutorial we will learn to,..."