Patterns and series are an integral part of our daily life. If we observe closely, we find that most aspects of life have a particular pattern. Thus, it is essential to understand and study these patterns to better understand the occurrences around us. Chapter 9- Arithmetic Progressions deals with the study of these patterns or series. An arithmetic progression is referred to a list of numbers in which each term is obtained by adding a specific number to the preceding term exclusive of the initial term. This specific number is called the common difference of arithmetic progression and can be positive, negative or zero.
It further talks about the different types of APs and how they progress. For example, there are two broadly classified as Arithmetic progressions, namely finite and infinite. These are based on the existence of an end-term or nth term.
The chapter then sheds light on the nth term of an arithmetic progression. The nth term, an, of the AP having its first term as a, and the common difference as d is given by:
an = a + (n – 1) d.
Here, an is also called the general term of the AP.
If an AP has m terms, then am represents the last term. The last term is also represented by the letter l.
The chapter concludes with a special mention of an important application of the Arithmetic Progression. It is used for calculating the sum of N terms of a series. This particular application finds great use in the real world, and hence, the students must go through this topic very thoroughly. For example, the following formula gives the sum of the first n terms of an AP:
S = 2n[2a + (n – 1) d ]