Progression is a sequence of numbers in a particular order. The arithmetic progression is the most commonly used sequence with easy to understand formulas.
If we observe in our regular lives, we come across progression quite often. Roll numbers of our class, days in a week or months in a year. Did you notice that counting numbers, even numbers or odd numbers, all follow a particular progression!
What is Progression?
It is a set of numbers in a particular matter, for example, consecutive numbers with a positive difference such as 2, 4, 6, 8. Here, numbers are continuously increasing with a difference of 2. This difference in arithmetic progression is called common difference. And it remains constant in the series. Therefore, If I ask you the fifth number in this series, you will immediately answer it as 10.
Similarly, the difference can be negative such as 5,4,3,2….
For simpler terms, you can figure out the next number. What if I ask you the 20th term of the series of 1,3,5,7..?
You can still calculate, but it consumes time and becomes difficult with increasing numbers. But if you follow arithmetic progression formula, it is an easy task for you! And guess what? You can figure out the formula for yourself!
Suppose, the series is 1,2,3,4,5.
The 1st term is 1. The common difference in this arithmetic progression is 1. Notice the 2nd term. It is the sum of 1st term plus the common difference. That is 1+1=2. Similarly, for 3rd term, it is the sum of 1st term plus twice the common difference. That is 1+ (2*1)= 3.
So, can we generalize this? We already have arrived at the arithmetic progression formula!
Let the Nth term which is to be found in an arithmetic progression be The first term be A. The common difference is D.
T= A+(N-1) D
The happy part is while learning for arithmetic progression; you also get to know about Harmonic progression! How? It is the reciprocal of the terms of Arithmetic progression. Like ½, 1/3, ¼, 1/5, 1/6 is the harmonic progression.
Identify the pattern and then understand how the problem is derived and you are done! Questions based on sum of series, the number of terms are frequent in exams. More concept building can be done from BYJUs application, where visuals and interesting demonstrations explain the progression formulas.