Sequences of Points, Circles and Line Segments -

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To create a sequence of points, circles or line segments on geogebra.org/classic, we use the sequence command.

The sequence command:

Let’s make a sequence of points, with coordinates $(n, n^2)$ , for values of $n$ between $1$ and $5$ . That is,

$\{(1,1), \quad (2,4), \quad (3,9), \quad (4,16), \quad (5,25)\}$

To generate this sequence of points, we type in:

Which yields the graph:

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

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

Sequences of Circles

To draw a sequence of circles we use the circle command. The circle command requires a center and a radius.

Lets make sequence of circles with center $(10,5)$ and with radius $n$ .

Try out the following command in the geogebra applet below:

Copy& paste: Sequence[Circle[(10,5),n],n,1,5]

Now try:

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

The final parameter changes the increment of $n$ 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.

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

Now see if you can reproduce the following diagrams:

Project 1

Project 2

ProJect 3

Solutions

Sequence of Line Segments

The following diagram uses the command Segment[<point>,<point>] to create a sequence of line segments. Observe the start/end point to a few of line segments to see the pattern of start and end points.

Solution

Draw your own sequence diagrams!

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