How do I find the expression for the nth term in a series of numbers?

First write down the series of numbers e.g.  8,  12,  16,  20.

Calculate the difference between each term in the series 12-8 = 4, 16-12 = 4,  20-16 = 4 This shows that the expression will begin with 4n as the difference is 4.  Next write out the series of number that would be in the expression '4n'. This would be: 4(1) = 4, 4(2) = 8, 4(3) = 12, 4(4) = 16. Now right the 4n sequence above the original sequence so it will be: 4  8  12  16 // 8 12 16 20 .  Caculate how to get from the first sequence to the second. This would be +4 as to get from 4 to 8 and 8 to 12 you need to add 4. Therefore the expression is 4n+4.  Always test this out afterwards e.g. 4(1)+4 = 8, 4(2)+4=12, 4(3)+4 = 16, 4(4)+4 = 20.  The sequence 8, 12, 16, 20 is the same as we started with so 4n+4 is the expression for the nth term.