What Does arithmetic progression Mean
Progression , which has its origin in the Latin progressio , is a concept that can be used to refer to a certain development, progress, advancement or succession . The arithmetic , moreover, is the branch of mathematics specializing in numbers and operations that can be performed with them.
From these ideas, we can focus on the notion of arithmetic progression . It must be borne in mind that, in the field of mathematics , progressions are sequences of numbers or terms that are related by some law.
An arithmetic progression , in this way, is made up of a series of numbers that have a constant difference when they are successive within the sequence in question. Let's look at a specific case:
The sequence 3, 7, 11, 15, 19 is an arithmetic progression whose constant difference is 4 . This can be seen if we carry out the following operations : 3 + 4 = 7 ; 7 + 4 = 11 ; 11 + 4 = 15 ; 15 + 4 = 19 . As can be seen, if we add 4 to each term , we will obtain the term that follows within the arithmetic progression.
The constant quantity that identifies an arithmetic progression is known as the difference or distance . This common difference can be a negative number: 8, 3, -2, -7, -12 is an arithmetic progression whose constant difference is -5 .
Another example of an arithmetic progression is the following: 152, 407, 662, 917, 1172 . In this case, the constant distance is 255 : 152 + 255 = 407 ; 407 + 255 = 662 ; 662 + 255 = 917 ; 917 + 255 = 1172 .
Applications of arithmetic progressions
Mathematics, unlike other sciences, has the particular trait of instilling fear in people who do not have a natural taste for numbers, but the reason is the way in which it is taught to us in our student years. In a strict sense, mastering calculations and equations is "as difficult" as understanding and being able to tell the stories of the heroes or to learn to use language with precision, respecting the rules of grammar and spelling, since each person has facility for a particular type of knowledge .
That said, numbers are present in our daily lives, as well as vestiges of human history and verb tenses; You just have to know how to detect them to make sense of mathematical concepts and learn to use them in a way that helps us live better. Without realizing it, every day we come across many concepts that at school we hated and we believed would never serve us; arithmetic progressions are no exception, as we will see below.
Suppose we have a bag of coins, all of the same value, and we need to know the total sum: the normal thing is to take them one at a time and group them to one side while we mentally perform the sum. Well, this operation is nothing more than an arithmetic progression in which the value of the distance is that of the coin .
On the other hand, in the making of crafts and in the design of many types of elements that we use for different purposes in everyday life, we also unconsciously take advantage of the bases of arithmetic progressions. For example, when building or drawing a pyramid-shaped object starting from pieces of the same size , it is normal to build a base of x pieces and, at each level, subtract a constant difference , until reaching the top.
In business, the arithmetic progression is also used frequently; such is the case of financial companies, which take advantage of this concept to calculate averages , applying their own knowledge of statistics.