One common type of series is the arithmetic series (also called an arithmetic progression). Each new term in an arithmetic series is the previous term plus a given number. For example this is an arithmetic series:
1+4+7+10+13+....
In this case each term is the previous term plus 3. The difference between each term (the 3 in this case) is called the "common difference" and is generally denoted by the letter d.
Here's another arithmetic series:
2+6+10+14+....
In this case d is 4, because that's what you add on to get each successive term.
There are many arithmetic series that have d=4. To specify which series we mean, we need to know one more piece of information: the value of the first term (usually called "a"). In the series above, a=2 and d=4.
If instead a=1 and d=4, the series must be this one:
1+5+9+13+.....
Here's another arithmetic series. What are a and d in this case?
5+7+9+11+....
If we're given a and d, then, that specifies a unique arithmetic series. All arithmetic series therefore have the following form:
a+(a+d)+(a+2d)+(a+3d)+....
Writing the series like that, we can see the formula for working out the value of any term. The first term is just a, for the second term we add d on once, for the third term we add d on twice, and so on. So for the 10th term, say, we'd add d on 9 times.
So in general we can say that the value of the nth term is a+(n-1)d.