Arithmetic Sequences lesson 1
1. Learn the tools
An arithmetic sequence begins 3, 7, 11, 15, 19 ...
In the input bar, type in the points for this sequence one at a time.
(1,3) (2,7) (3,11) (4,15) (5,19)
Use the four arrow tool on the y-axis to adjust the axis.
2. Make a graph of your own arithmetic sequence. Type in the first five points.
3. Type in the first five points of the arithmetic sequence that has formula
The first point is (1, 3(1)+2) which is (1, 5). etc. You will need to adjust the axes to see all the points.
4. Generating a sequence of numbers
We can generate a whole sequence with a single command. Try these two commands out to see what they do:
- sequence(3,6)
- sequence(3n+2,n,1,5)
5. Generating a sequence of points
The sequence command sequence(expression,variable,start,end) allows us to generate a sequence of any GeoGebra objects - such as points, lines, circles, polygons etc.
To generate a sequence of points the 'expression' is the (x,y) coordinates of the points.
To generate the sequence of points for the sequence the x coordinate is 'n' and the y coordinate is '3n+2'. Type this command into the input bar:
sequence((n,3n+2),n,1,5)
This generates the first five points. Try it out. Change the '5' to a '10' to generate the first ten points.6. Type in a sequence of points using the sequence command that generates a sequence that decreases. Make sure all the points can be seen in the graphing window by adjusting the window with the four arrow tool.
7. It's possible to make sequences of all kinds of objects. Follow these instructions:
Plot the points A=(1,1) and B=(4,1)
Type in the command
sequence(polygon(A,B,n),n,3,8)
What does the 'n' stand for in the command in question 7?
8. Try out some of the commands in the pdf file attached on GeoGebra classic.
Go to the hamburger menu (top right), View, Input Bar to open the long input bar.
