1. Introduction to arithmetic progression

Let us see a moment to look around our surrounding. We might have observed specific patterns in nature, such as the patterns in the sunflowers, seashell covers and a honeycomb's holes. (Click to know more)

 

 

We can observe similar patterns in mathematics as well. For instance, say the Fibonacci series, the Arithmetic Progression, and the Geometric Progression.

 

In this chapter, we deep dive and explore the Arithmetic Progression with examples.

 

Let us see a scenario before we go into Arithmetic Progression.

From the above scenario, we can understand that the number sequence undergoes a certain sequence or a pattern by the constant common difference. And this kind of sequence is called arithmetic progression.

 

1. In a theatre, the arrangement of seats form an arithmetic progression. For instance, the first row might have \(12\) seats; the second row has \(14\) seats, and the third row contains \(16\).

 

 

2. Most of the banks provide a fixed interest amount for saving account. For example, if we keep \(₹\)\(1000\) in a saving account for one year, we would receive a specific percentage amount as interest at the end of the year. So, this saving amount plus interest amount added will become our new saving amount that will interest the proceeding years.

 

 

3. When you ride a taxi, you will be charged an initial rate and then a per mile or kilometres. And for every kilometre, you will be charged a certain amount extra plus the initial rate. This shows that how the arithmetic sequence works when determining the cost.

 

 

4. The lowest temperatures (in degrees Celsius) recorded in a city for a week in December, given in ascending order are:

 

\(– 4.1, – 3.8, – 3.5, – 3.2, – 2.9, – 2.6, – 2.3\)

 

 

Now we learned about the fundamentals of Arithmetic Progression \((A.P)\). In the upcoming lessons, we will learn the terms of Arithmetic Progression \((A.P).\) and practice the same concept.