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

PoojaMoolya at 09:13, 10 October 2019

2019-10-10T09:13:21Z

Madhurig at 05:56, 26 September 2019

2019-09-26T05:56:20Z

Madhurig at 05:52, 26 September 2019

2019-09-26T05:52:31Z

Nancyvarkey at 05:03, 6 September 2019

2019-09-06T05:03:49Z

Madhurig at 09:53, 4 September 2019

2019-09-04T09:53:46Z

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Madhurig: Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- || '''Slide Number 1''' '''Title slide ''' || Welcome to the Spoken Tutorial on '''Sequences in GeoGebra'''. |- || '''Slide..."

2019-09-04T08:11:16Z

Created page with "{|border=1 ||'''Visual Cue''' ||'''Narration''' |- || '''Slide Number 1''' '''Title slide ''' || Welcome to the Spoken Tutorial on '''Sequences in GeoGebra'''. |- || '''Slide..."

New page

{|border=1
||'''Visual Cue'''
||'''Narration'''
|-
|| '''Slide Number 1'''

'''Title slide '''
|| Welcome to the Spoken Tutorial on '''Sequences in GeoGebra'''.
|-
|| '''Slide Number 2'''

'''Learning Objectives'''

|| 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
|-
|| '''Slide Number 3'''

'''System Requirement'''
|| To record this tutorial, I am using;
* '''Ubuntu Linux OS''' version 16.04
* '''GeoGebra''' version 5.0438.0-d
|-
|| '''Slide Number 4'''

'''Pre-requisites'''

'''https://spoken-tutorial.org'''
|| To follow this tutorial, learner should be familiar with '''GeoGebra''' interface.

For the prerequisite '''GeoGebra''' tutorials, please visit this website.
|-
|| Show the list of commands.
|| The '''commands''' used in the tutorial are provided in the '''Code Files''' link.
|-
|| Cursor on '''GeoGebra''' interface.
|| I have already opened '''GeoGebra''' interface.
|-
|| Point to '''Algebra''' and '''Graphics views'''.
|| We will first resize and place the '''Algebra view''' above the '''Graphics view'''.
|-
|| Place the cursor on '''Algebra view''''s title bar.
|| Place the cursor on the '''Algebra view''''s title bar.
|-
|| Click and drag the mouse.

Point to the rectangular outline.

Release the mouse.
|| Click and drag the mouse.

When you see a rectangular outline, release the mouse.
|-
|| Drag the boundary.
|| Drag boundary to see the '''Graphics view''' clearly.
|-
|| Cursor on '''GeoGebra''' interface.
|| To create sequences I will open the '''Spreadsheet view'''.
|-
|| Click on '''View''' menu >> click on '''Spreasheet''' check-box
|| Click on''' View''' menu and select '''Spreasheet''' check-box.
|-
|| '''Cursor on the Spreadsheet view'''.
|| '''Spreadsheet view''' opens next to the '''views'''.
|-
|| Drag boundary of the '''Spreadsheet view'''.
|| Drag the boundary to see the '''Spreadsheet view''' clearly.
|-
|| Type 2 in cell '''A1''' >> press '''Enter'''.
|| In cell '''A1''' type 2 and press '''Enter'''.
|-
|| Type '''A1+2''' >> press''' Enter.'''

Point to cell''' A2.'''
|| In the cell '''A2''' type '''A1+2''' and press '''Enter'''.

Four is displayed in the cell '''A2'''.
|-
|| Cursor in '''cell A2'''.
|| Now we will create a sequence of numbers using the formula entered in cell '''A2'''.
|-
|| Place cursor at the corner of cell A2 drag the fill handle.

Point to the sequence of even numbers.
|| 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.
|-
|| Cursor in '''Spreadsheet view'''.
|| Now we will create a list for this sequence.
|-
|| Select the cells from '''A1 '''to '''A15 '''by dragging.

Right-click to open the context menu.
|| Select the cells from '''A1 '''to '''A15 '''by dragging.

When we right-click on the selected cells, a context menu opens.
|-
|| Select '''Create''' >> '''List'''.

Point to the list '''l1'''in the '''Algebra view'''.
|| In the menu select '''Create''' and then '''List'''.

A list '''l1''' is created in the '''Algebra view'''.
|-
|| Drag boundary of the '''Algebra view'''.
|| Drag the boundary of the '''Algebra view''' to see the complete list.
|-
|| Point to the numbers in the list l1.
|| '''l1''' contains a list of even numbers from 2 to 30.
|-
|| Click on '''Close''' button.
|| Close the '''Spreadsheet view''' by clicking on the '''Close''' button.
|-
|| Right-click on '''l1''' in '''Algebra view'''.
|| We will rename '''l1''' as '''Evens'''.

In the '''Algebra view''' right-click on '''l1'''.
|-
|| From the sub-menu, select '''Rename'''.
|| From the sub-menu, select '''Rename'''.
|-
|| In the '''Rename''' text box, type '''Evens''' >> click '''OK''' button.
|| In the '''Rename''' text box, type '''Evens''' and click on the '''OK''' button.
|-
|| Cursor on the interface.
|| We can create a similar sequence for odd numbers using the '''Sequence command'''.
|-
|| Type, '''Odds=Sequence'''.

Point to various options of ''' Sequence command.'''
|| In the '''input bar''' type''' Odds=Sequence'''.

Various options appear.

Select the option '''Sequence(<Expression>, <Variable>, <Start Value>, <End Value>)'''.
|-
|| Type '''Expression''' as '''2n+1'''

Press '''Tab''' key.

Type '''Variable''' as '''n''',

Press '''Tab '''key >> type''' Start Value''' as 0.

Press '''Tab''' key >> type '''End Value''' as 15.

Press '''Enter'''.
|| 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 '''End Value''' as 15.

And then press '''Enter'''.
|-
|| Point to the '''Odds''' sequence.
|| Observe the sequence of odd numbers from 1 to 31 in the '''Algebra view'''.
|-
|| Cursor on the interface.
|| We will use the '''Sequence command''' to show a series of points in the '''Graphics view'''.
|-
|| '''L_1=sequence[(n,0),n, 1,10]'''

Highlight the command in the '''input bar'''.
|| 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'''.
|| Drag the '''Graphics view''' if you cannot see the points on the x-axis.
|-
|| Cursor on the '''x-axis.'''

Point to the coordinates in the '''Algebra view.'''
|| We see a series of points on the x-axis from 1 to 10.

Coordinates of the points are shown in the '''Algebra view'''.
|-
|| Move the cursor on the points.
|| Let us change the position of these points.
|-
|| In '''Algebra view''' double click on the list '''L1'''.

Point to the dialog box.
|| In the '''Algebra view '''double click on the list '''L1'''.

The '''Redefine''' text box appears.
|-
|| Type '''(0,n)''' in place of '''(n,0)''' >> click on '''OK''' button.

Cursor on the points.

Highlight the points in list L1
|| In the box change (n,0) to (0,n) and click on the '''OK''' button.

Observe that the points move to y-axis.

Note the changes in the list '''L1'''.
|-
|| Click on '''Zoom Out''' tool >> Click in '''Graphics view''' to zoom out.
|| Using '''Zoom Out''' tool, click in '''Graphics view''' to see all the points on the y-axis.
|-
|| Double click on list '''L1''' in the''' Algebra view.'''

Type '''(n,n)''' in place of '''(0,n)'''>> click on '''OK''' button.
|| Again double-click on the list '''L1''' in the '''Algebra view'''.

In the '''Redefine''' text box, change '''(0,n)''' to '''(n,n)''' and click on the '''OK''' button.
|-
|| Cursor on the points.

Highlight the points in list L1
|| Observe that the coordinates of the points change to '''(n,n)'''.

Note the changes in the list '''L1'''.
|-
|| Cursor on the interface.
||
* We will now a draw line segment to join (0,0) and (n,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'''.
|-
|| '''Sequence[Segment((0, 0), (n, n)), n, 0, 10, 1]'''
|| In the '''input bar''', type the following '''command''' and press '''Enter'''.
|-
|| Point to the lines.
|| Observe that a line is drawn to join the points.

A new list '''l1''' is generated in the '''Algebra view'''.
|-
|| '''Slide Number 5'''

'''Assignment'''
|| As as assignment:

Use the '''Sequence command''' to show a list of squares of numbers from 1 to 10.
|-
|| Cursor on the interface.
|| We will create arithmetic progression (AP) and geometric (GP)progression using the '''Sequence command'''.
|-
|| Scroll and show the Additional material.
|| For more information on AP and GP, please see the '''Additional Material''' provided along with this tutorial.
|-
|| Click on '''File''' >> '''New Window'''.
|| I will open a new '''GeoGebra''' window.
|-
|| '''AP=Sequence[a+(n-1)d, n,0,10]'''

Press '''Enter'''.
|| In the '''input bar''', type the following '''command''' and press '''Enter'''.
|-
|| Point to the dialog box.

Click on '''Create Sliders''' button.
|| '''Create Sliders''' dialog box appears.

Click on '''Create Sliders''' button.
|-
|| Point to the sliders in the''' Graphics view.'''
|| Number sliders '''a''', '''n''' and '''d''' are created in the '''Graphics view'''.
|-
|| Point to the sequence '''AP''' in the''' Algebra view'''.
|| Observe that a new sequence '''AP '''is generated in the '''Algebra view'''.
|-
|| Drag the boundary of the '''Algebra view'''.
|| Drag the boundary to see the '''Algebra view''' clearly.
|-
|| '''Point to the list AP.'''
|| This '''command''' has generated a series of numbers '''a+(n-1)d'''.

Here '''n''' goes from 0 to 10 and '''a''' and '''d''' go from -5 to 5.
|-
|| Drag the''' sliders a''' and '''d'''.

Point to the sequence '''AP'''.
|| Drag the '''sliders a''' and '''d'''.

As we drag the sliders, observe the changes in the sequence '''AP'''.
|-
|| Point to the sequence '''AP''' >> ''' Graphics view'''.
|| Notice that, sequence '''AP '''does have not any representation in the '''Graphics view'''.
|-
|| Type in the '''input bar''', '''Sequence[(n, a + d n), n, 0, 10]''' >> press '''Enter'''.
|| In the '''input bar''', type in the following '''command''' and press '''Enter'''.
|-
|| Observe the points in the '''Graphics view ''' >> ''' Algebra view'''.
|| Observe that a list of points '''l1''' is generated for the sequence '''AP'''.
|-
|| Click on the '''Zoom Out''' tool >> click in the '''Graphics view'''.
|| Click on the '''Zoom Out''' tool and click in the '''Graphics view''' to see all the points.
|-
|| Cursor on the interface.
|| Let us find the sum of n terms of the series.
|-
|| '''Sum=n/2{2a+(n-1)d}''' >> Press '''Enter'''.

Point to the '''Algebra view'''.
|| In the '''input bar''', type the following '''command''' and press '''Enter'''.

Sum of n terms is displayed in the '''Algebra view'''.
|-
|| Type''' a+dx '''and press''' Enter'''.

Point to '''f(x)''' in the '''Algebra view'''.
|| Now type '''a+dx''' and press '''Enter'''.

A line '''f of x''' is drawn to join the points of the sequence '''AP'''.
|-
|| Drag sliders '''a''' and '''d'''.
|| Again drag sliders '''a''' and '''d''' to see the changes.
|-
|| Cursor in''' GeoGebra interface'''.
|| Now we will generate a geometric progression.
|-
|| Press '''Ctrl + A''' to select all objects.

Press '''Delete''' key on the key board.
|| Let us delete all the objects from the '''views'''.
|-
|| '''GP=Sequence[(b r ^ n), n, 0, 10]'''
|| In the '''input bar''' type, the following '''command''' and press '''Enter'''.
|-
|| Point to the dialog box.

Click on '''Create Sliders''' button.
|| '''Create Sliders''' dialog box appears.

Click on '''Create Sliders''' button.
|-
|| Point to the sliders in the '''Graphics view'''.
|| Sliders '''b''', '''r''' and '''n''' are created in the '''Graphics view'''.
|-
|| Drag boundary of the '''Algebra view'''.
|| Drag the boundary to see the '''Algebra view''' clearly.
|-
|| Point to the sequence in the''' Algebra view'''.
|| 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'''.
|| Drag the sliders '''b''' and''' r''' to see the changes in the geometric progression.
|-
|| '''GP=Sequence[(n,b r ^ n), n, 0, 10]'''

Move the cursor on the points.
|| Type the following '''sequence command''' and press '''Enter'''.

A series of points from 1 to 10 are plotted in the first quadrant.
|-
|| Type '''b r ^ x '''and press '''Enter'''.
|| Now type '''b r''' raised to the power of '''x''' ( '''b r ^ x)''' and press '''Enter'''.

Observe that a line is drawn to join the points.
|-
|| Drag the sliders''' b '''and''' r.'''

Point to the curve g(x)
|| 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.
|-
|| '''Slide Number 6'''

'''Assignment.'''
|| As an assignment:

Find the sum of n terms in a geometric progression.
|-
|| Cursor on the interface.
|| Now we will divide a line segment into parts using the '''Sequence command'''.
|-
|| Click on '''File''' >> '''New Window'''.
|| I have opened a new '''GeoGebra''' window.
|-
|| Click on '''Segment with Given Length''' tool >> click in '''Graphics view'''.

Point to the text box.
|| 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 >> click OK.
|| In the '''Length''' text box, type 10 and click '''OK'''.
|-
|| Click on '''Slider'''tool >> click in the '''Graphics view'''.
|| Now we will create a number slider n.

Click on '''Slider''' tool and click in the '''Graphics view'''.
|-
|| Type '''Name''' as '''n'''

Type '''Min''' as 1, '''Max''' as 10, '''Increment''' as 1.

Click '''OK''' button.
|| 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.
|-
|| '''sequence[A+(B-A)/n*k, k,1,n-1]'''
|| In the '''input bar''' type the following '''command'''.
|-
|| Point to the command.

Press Enter.
|| 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''' to see the partitions.
|| Drag the slider '''n''' and see the partitions in the segment '''AB'''.
|-
|| '''Ctrl + A '''to select all objects.

Press''' Delete '''key on the key board.
|| Let us delete all the objects from the views.
|-
|| Cursor on the interface.
|| We can use the '''Sequence command''' along with additional '''commands'''.
|-
|| '''Sequence[Circle[(0,0) , r ], r , 0 , 5 , 0.25] '''
|| For example, type the following '''command''' and press '''Enter'''.

Using this '''command''' we have drawn concentric circles with origin at (0,0) and radius r.

Here '''r''' goes from 0 to 5 in the increments of 0.25.
|-
|| Point to '''l1'''.

In the '''Algebra view''' right-click on '''L1''' >> select '''Delete'''.
|| Let us delete '''l1'''.

In the '''Algebra view''' right-click on '''l1''' and select '''Delete'''.
|-
|| '''Sequence[x^2 + c x, c, -5, 5, 0.5]'''
|| Next type this '''command''' and press '''Enter'''.

Using this '''command''' we have drawn a family of parabolas '''x^2+cx'''.

Here c goes from -5 to 5 in the increments of 0.5.
|-
|| '''Slide Number 7'''

Assignment

Generate a sequence to draw:

* Polygons at (0,0) and (1,0) of n sides, where n goes from 3 to 10.

Hint: type [Polygon[(point), (point), n], n, start value of n, end value of n]

|| As an assignment:

Generate a sequence to draw polygons.
|-
|| '''Slide Number 8'''

'''Assignment'''

Generate sequences to draw:

* Parabolas x^2+c where c goes from -5 to 5 in increments of 0.5
* Parabolas c x^2+ 2c x-1 </nowiki>where c goes from -5 to 5 in increments of 0.5
|| And generate sequences to draw parabolas.
|-
||
|| Let us summarize
|-
|| '''Slide Number 9'''

'''Summary'''
|| 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'''
|-
|| '''Slide Number 10'''

'''About Spoken Tutorial project'''
|| The video at the following link summarizes the '''Spoken Tutorial project'''.

Please download and watch it.
|-
|| '''Slide Number 11'''

'''Spoken Tutorial workshops'''
|| The ''Spoken Tutorial Project ''' team:

* conducts workshops using spoken tutorials and
* gives certificates on passing online tests.

For more details, please write to us.
|-
|| '''Slide Number 12'''

'''Forum for specific questions:'''

* Do you have questions in THIS '''Spoken Tutorial'''?
* Please visit this site
* Choose the minute and second where you have the question.
* Explain your question briefly
* Someone from our team will answer them.
|| Please post your timed queries on this forum.
|-
|| '''Slide Number 13'''

'''Acknowledgement'''
|| Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.
|-
||
|| This is Madhuri Ganapathi from, IIT Bombay signing off.

Thank you for watching.
|-
|}

@@ Line 61: / Line 61: @@
 || To create sequences, I will open the '''Spreadsheet view'''.
 |-
-|| Click on '''View''' menu >> click on '''Spreasheet''' check-box
+|| Click on '''View''' menu >> click on '''Spreadsheet''' check-box
-|| Click on '''View''' menu and select '''Spreasheet''' check-box.
+|| Click on '''View''' menu and select '''Spreadsheet''' check-box.
 |-
 || '''Cursor on the Spreadsheet view'''.
@@ Line 285: / Line 285: @@
 || This '''command''' has generated a series of numbers  '''a plus n minus 1 into d'''  .
-Here '''n''' goes from 0 to 10 and '''a''' and '''d''' go from -5 to 5.
+Here '''a''' and '''d''' go from -5 to 5.
 |-
 || Drag the''' sliders a''' and '''d'''.
@@ Line 365: / Line 365: @@
 || Type the following '''Sequence command''' and press '''Enter'''.
-A series of points from 1 to 10 are plotted in the first quadrant.
+A series of points from 0 to 10 are plotted in the first quadrant.
 |-
 || Type  '''b r ^ x ''' >> press '''Enter'''.

@@ Line 23: / Line 23: @@
 || To record this tutorial, I am using;
 * '''Ubuntu Linux OS''' version 16.04
-* '''GeoGebra''' version 5.0438.0-d
+* '''GeoGebra''' version 5.0.438.0-d
 |-
 || '''Slide Number 4'''

@@ Line 514: / Line 514: @@
 '''Spoken Tutorial workshops'''
-|| The ''Spoken Tutorial Project ''' team:
+|| The '''Spoken Tutorial Project''' team:
 * conducts workshops using spoken tutorials and

@@ Line 13: / Line 13: @@
 || In this tutorial we will learn to,
-* Use spreadsheet view to create simple sequences
+* Use '''spreadsheet view''' to create simple sequences
-* Use commands to create sequences and progressions
+* Use '''commands''' to create sequences and progressions
 * Divide the line segment into parts
-* Use '''Sequence''' command along with other commands
+* Use '''Sequence command''' along with other '''commands'''
 |-
 || '''Slide Number 3'''
@@ Line 133: / Line 133: @@
 Point to various options of '''Sequence command'''.
-|| In the '''input bar''' type '''Odds=Sequence'''.
+|| In the '''Input bar''' type '''Odds=Sequence'''.
 Various options appear.
@@ Line 171: / Line 171: @@
 Highlight the command in the '''input bar'''.
-|| In the '''input bar''' type the following '''command'''.
+|| In the '''Input bar''' type the following '''command'''.
 This '''command''' draws points at (n,0) where '''n''' goes from 1 to 10.
@@ Line 193: / Line 193: @@
 Point to the dialog box.
-|| In the '''Algebra view '''double click on the list '''L1'''.
+|| In the '''Algebra view '''double-click on the list '''L1'''.
 The '''Redefine''' text box appears.
@@ Line 230: / Line 230: @@
 || Cursor on the interface.
 ||
-* We will now a draw line segment to join zero comma zero((0,0)) and n comma n((n,n)).
+* We will now a draw line segment to join zero comma zero((0,0)) and n comma n((n,n))
 * where n goes from 0 to 10 in the increments of 1.
@@ Line 236: / Line 236: @@
 |-
 || '''Sequence[Segment((0, 0), (n, n)), n, 0, 10, 1]'''
-|| In the '''input bar''', type the following '''command''' and press '''Enter'''.
+|| In the '''Input bar''', type the following '''command''' and press '''Enter'''.
 |-
 || Point to the lines.
@@ Line 251: / Line 251: @@
 |-
 || Cursor on the interface.
-|| We will create arithmetic progression (AP) and geometric (GP)progression using the '''Sequence command'''.
+|| We will create arithmetic progression '''(AP)''' and geometric progression '''(GP)''' using the '''Sequence command'''.
 |-
 || Scroll and show the '''Additional material'''.
@@ Line 262: / Line 262: @@
 Press '''Enter'''.
-|| In the '''input bar''', type the following '''command''' and press '''Enter'''.
+|| In the '''Input bar''', type the following '''command''' and press '''Enter'''.
 |-
 || Point to the dialog box.
@@ Line 272: / Line 272: @@
 |-
 || Point to the sliders in the''' Graphics view.'''
-|| Number sliders '''a''', '''n''' and '''d''' are created in the '''Graphics view'''.
+|| Number sliders '''a, n''' and '''d''' are created in the '''Graphics view'''.
 |-
 || Point to the sequence '''AP''' in the''' Algebra view'''.
@@ Line 298: / Line 298: @@
 |-
 || Type in the '''input bar''',  '''Sequence[(n, a + d n), n, 0, 10]''' >> press '''Enter'''.
-|| In the '''input bar''', type in the following '''command''' and press '''Enter'''.
+|| In the '''Input bar''', type in the following '''command''' and press '''Enter'''.
 |-
 || Observe the points in the '''Graphics view ''' >> ''' Algebra view'''.
@@ Line 312: / Line 312: @@
 Point to the '''Algebra view'''.
-|| In the '''input bar''', type the following '''command''' and press '''Enter'''.
+|| In the '''Input bar''', type the following '''command''' and press '''Enter'''.
 Sum of '''n''' terms is displayed in the '''Algebra view'''.
@@ Line 324: / Line 324: @@
 |-
 || Drag sliders '''a''' and '''d'''.
-|| Again drag sliders '''a''' and '''d''' to see the changes.
+|| Again, drag sliders '''a''' and '''d''' to see the changes.
 |-
 || Cursor in''' GeoGebra interface'''.
@@ Line 335: / Line 335: @@
 |-
 ||  '''GP=Sequence[(b r ^ n), n, 0, 10]'''
-|| In the '''input bar''' type, the following '''command''' and press '''Enter'''.
+|| In the '''Input bar''' type, the following '''command''' and press '''Enter'''.
 |-
 || Point to the dialog box.
@@ Line 345: / Line 345: @@
 |-
 || Point to the sliders in the '''Graphics view'''.
-|| Sliders '''b''', '''r''' and '''n''' are created in the '''Graphics view'''.
+|| Sliders '''b, r''' and '''n''' are created in the '''Graphics view'''.
 |-
 || Drag boundary of the '''Algebra view'''.
@@ Line 422: / Line 422: @@
 |-
 ||  '''sequence[A+(B-A)/n*k, k,1,n-1]'''
-|| In the '''input bar''' type the following '''command'''.
+|| In the '''Input bar''' type the following '''command'''.
 |-
 || Point to the command.
@@ Line 436: / Line 436: @@
 |-
 || Drag the slider '''n''' to see the partitions.
-|| Drag the  ''' slider n''' and see the partitions in the segment '''AB'''.
+|| Drag the   slider '''n''' and see the partitions in the segment '''AB'''.
 |-
 || '''Ctrl + A '''to select all objects.
 Press '''Delete''' key on the key board.
-|| Let us delete all the objects from the views.
+|| Let us delete all the objects from the '''views'''.
 |-
 || Cursor on the interface.
@@ Line 465: / Line 465: @@
 Using this '''command''' we have drawn a family of parabolas '''x^2+cx'''.
-Here c goes from -5 to 5 in the increments of 0.5.
+Here '''c''' goes from -5 to 5 in the increments of 0.5.
 |-
 || '''Slide Number 7'''
@@ Line 499: / Line 499: @@
 '''Summary'''
 || In this tutorial we have learnt to,
-* Use spreadsheet view to create simple sequences
+* Use '''spreadsheet view''' to create simple sequences
 * Use '''commands''' to create sequences and progressions
 * Divide the line segment into parts