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This applet investigates simple linear sequences and how to find the general nth term
Instructions below    A smaller version of this applet    light background    Waldomaths video    See also: Simple quadratic sequences    Harder quadratic sequences    Cubic sequences
[Simple linear sequences]

This program starts with a challenge. What is the rule for the sequence of numbers shown?
By moving the two sliders left and right (by clicking and dragging with the mouse) you can try different rules, to see which one fits the sequence given.
To begin with, the sequences always increase (eg 1,4,7,10...). When you feel you understand these types of sequences, then you can make the problem a little harder by also looking at decreasing sequences by removing the tick by the 'increasing sequences only' box at the top of the page.

Each time you click the 'New problem' button you will get a new sequence to investigate.
On this larger version there is also a graph of the points in the sequence. You will see that all the points are in a straight line. This is why sequences like this are called linear sequences.
Have a go! You'll soon learn the idea by experimenting for yourself.

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