## Writing formulas from sequences

 7, 10, 13, 16, _____, _____, ... Take a look at the sequence of numbers above. How do the numbers grow from one to the next? Do you see a pattern? Once you see that the numbers get bigger by 3 each time, it is easy to see that the next two terms in the sequence are 19 and 22. The sequence becomes 7, 10, 13, 16, 19, 22, ... This sequence is called an arithmetic sequence because the numbers change by adding a constant number each time. What if you wanted to know what would be the 50th term in this sequence? You could either continue making the list until the 50th number or you can write a formula. The applet below will show you how to create the formula for any arithmetic sequence.

Directions:

1. Create a sequence.
2. Show as many terms as you want to see.
3. Use the nth term slider until you find the formula
4. Click "Show expression" to see the formula.

Duane Habecker, Created with GeoGebra. This applet is based on an original applet created by Robert Fant.