The Sequence Command

The sequence command of geogebra, combined with other commands, yields some fun diagrams!

The sequence command:

Let’s make a sequence of points, with coordinates , for values of between and . That is,

   

To generate this sequence of points, we type in:

 

 

 

Which yields the graph:

You can try that out on the geogebra applet below. You  many be able to copy, paste this command:

Sequence[(n,n^2),n,1,5,1]

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Sequences of Circles

Now suppose we want to draw a sequence of circles. The circle command requires a centre and a radius.

 

 

 

Suppose we make a sequence of circles with centre and with radius .

Try out the following command in the geogebra applet below:

 

 

 

To copy paste use: Sequence[Circle[(10,5),n],n,1,5]

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Geogebra applet:

If that worked for you, try out

Sequence[Circle[(10,5), n], n, 1, 5, 0.1]

The final parameter changes the increment of from the default value 1 to 0.1. More steps between 1 and 5 – more circles.

Make some of your own

Use the geogebra applet to generate your own sequence of circles.

1. Make a sequence where the centre of the circle is constant, but the radius changes.
2. Make a sequence where the centre of the circle changes, but the radius is constant.
3. Make a sequence where the centre and the radius both change.

Figure out the sequence command

Now see if you can reproduce the following diagrams:

Project 1

Project 2

ProJect 3

Solutions

1. Sequence[Circle[(n, n), n], n, 1, 5, 0.1]
2. Sequence[Circle[(n, 5), n], n, 1, 5, 0.05]
3. Sequence[Circle[(12 + n, 5), n], n, 1, 5, 0.05]