# Nth Term of a Simple Linear Sequence

This applet investigates simple linear sequences (also known as arithmetic sequences or arithmetic progressions) and how to find the general `n`th term by looking at the common difference between two terms

###### Author and programmer: Ron Barrow

UK Years 7-11, Ages 11-16, KS3, KS4 Higher and Foundation GCSE Mathematics - Number and Algebra

TweetInstructions below See also: Simple quadratic sequences Harder quadratic sequences Cubic sequences

## How to Use this Applet

This program starts with a challenge. What is the `n`th term 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. If the "show graph" box is checked then 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. You can turn off the working at the "show working" box to test yourself, and you can go back and start again by clicking the "reset" button. Have a go! You'll soon learn by experimenting for yourself.