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Arithmetic Progression – A Rising Sequence

Let’s learn about A.P and A.M in this topic. It’s an important topic in Mathematics. So let’s begin. Arithmetic Progression (AP) is defined as an ascending sequence of numbers where the difference between any two consecutive numbers is a constant. For example, the natural number sequence: 1, 2, 3, 4, 5, 6,… is an AP with a common difference of one between two consecutive terms (say, 1 and 2). (1 – 2) Even when dealing with odd and even numbers, the common difference between two consecutive terms is equal to 2.

Following the concept of arithmetic progression, how to find the ‘n’-th term and the sum of ‘n’ consecutive terms is explained using well-illustrated examples. The ‘difference’ is the fixed number that is added to the number in order to obtain the sequence.

What is Arithmetic Mean?

The arithmetic mean is also known as the mean or arithmetic average. Arithmetic mean is calculated by adding all the numbers in a given data set and then dividing the total number of items in that set by the total number of items in that set. For evenly distributed numbers, the arithmetic mean is equal to the number in the middle. Furthermore, the arithmetic mean is calculated using a variety of methods that are dependent on the amount of data and the distribution of the data.

Formula For Arithmetic Mean

AM = Sum of all the values / Total number of values

Let us look at an example where we can see the use ofarithmetic mean. Because 6 + 8 + 10 = 24 and 24 divided by 3 [there are three numbers] equals 8, the mean of the numbers 6, 8, 10 is 8. The arithmetic mean retains its position in calculating a stock’s average closing price for a given month. Assume a month consists of 24 trading days. How do we compute the mean? To calculate the arithmetic mean, add all of the prices together and divide by 24.

Types of Progressions

There are three types of progressions in mathematics. They are as follows:

  • Arithmetic Progression (AP)
  • Geometric Progression (GP)
  • Harmonic Progression (HP)

A progression is a type of sequence for which a formula for the nth term can be obtained. With simple formulas, the Arithmetic Progression is perhaps the most commonly used sequence in mathematics. Let’s take a look at the three types of definitions it has.

Definition 1: A mathematical sequence wherein the difference between successive terms is always a constant.

Definition 2: An arithmetic sequence or progression is a number sequence in which the second number is obtained by adding a fixed number to the first one for each consecutive pair of terms.

Definition 3: The common difference of an AP is the constant which must be added to any term of an AP to get the next term. Consider the arithmetic sequence 1, 4, 7, 10, 13, 16,…, which has a common difference of 3.

Applications of Arithmetic Progression

Stacking cups, chairs, bowls, and so on. (Anything can be stacked, but the situation changes when one thing fits inside the other.) The concept is to compare the number of objects to the object’s height.

Pyramid-like patterns in which objects increase or decrease in a consistent manner. Seats in a stadium or an auditorium are two options. Assume that each row’s seats are decreasing by four from the previous row.

Seating is arranged around tables. Consider a restaurant. A square table seats four people. When two square tables are joined together, a total of six people can be seated. Eight people can be seated when three square tables are joined together. You can also use a rectangular table and begin with 6 seats. To understand more about the topic in a better way, you can visit Cuemath.

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