We will look at three types of progressions called Arithmetic, Geometric and Harmonic Progression. Before we start looking at the intricacies of these let us understand what is meant by series. A series is a collection of numbers which may or may not terminate at some point. The first set of series that terminate is called finite series and the second one that do not terminate is called infinite series. In the theoretical sense an infinite series conveys that the number of elements in the series are so large that it is practically uncountable. Generally, series are expressed in an abridged form in terms of a general term known as n^{th} term. Therefore, given a series we can obtain its n^{th} term or else given an n^{th} term we can obtain the different elements of that series. For example, consider a simple n^{th} term which is:
If we substitute n = 1, the value of T_{n=1} will be
If we substitute n = 2, the value of T_{n=2} will be
If we continue to substitute different values for n, like we did above, we get different values of this particular series. This is an example of infinite series, whereas a series like 1, 2, 3, 4, 5, 6 is an example of finite series. The general term is given by T_{n} = n + 1, where n takes values from 0 to 5. After looking at these two examples we find that a series is finite or infinite depending on the values taken by n. In other words, a series terminates depending on the extent of values taken by n.