Arithmetic Progression

Arithmetic Progression

Arithmetic Progression (AP) is a sequence of numbers in a particular order. If we observe in our regular lives, we come across progression quite often. For example, Roll numbers of a class, days a week or months in a year. Did you notice that counting numbers, even or odd numbers, all follow a particular pattern? This pattern of series and sequences has been generalized in Maths as progressions. Let us learn here AP definition, important terms such as common difference, the first term of the series, nth term and sum of nth term formulas along with solved questions based on them.

Definition

In mathematics, there are three different types of progressions. They are:

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

A progression is a special type of sequence for which it is possible to obtain a formula for the nth term.  The Arithmetic Progression is the most commonly used sequence in maths with easy to understand formulas.  Let us see its three different types of definition.

Definition 1: It is a mathematical sequence in which the difference between two consecutive terms is always a constant and it is abbreviated as AP.

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

Definition 3: The fixed number that must be added to any term of an AP to get the next term is known as the common difference of the AP.

Now, let us consider the sequence, 1, 4, 7, 10, 13, 16,… is considered as an arithmetic sequence with common difference 3.

General Form of an A. P

Consider an AP to be: a1, a2, a3, ……………., an

Position of Terms	Representation of Terms	Values of Term
1	a1	a + d = a + (1-1) + d
2	a2	a + 2d = a + (2-1) + d
3	a3	a + 3d = a + (3-1) + d
4	a4	a + 4d = a + (4-1) + d
.	.	.
.	.	.
.	.	.
.	.	.
n	an	a + (n-1)d