What is Arithmetic Progression?

An arithmetic progression is a numerical sequence formed by adding a fixed number to the prior term beginning with the first term so that the difference between the subsequent terms remains constant. It is abbreviated as A.P. Some examples of arithmetic progression are,

• 1, 4, 7, 10, 13, …
• 12, 7, 2, −3, −8, …
• −9, −7, −5, −3, …

First Term and Common Difference

If a sequence a₁,a₂,a₃,a₄,…..,a_n is an A.P. with a common difference d, then

a₂ − a₁ = d

a₃ − a₂ = d

a₄ − a₃ = d

.

.

.

a_n − a_n-1 = d and so on. 

and a₁ is the first term of the Sequence which is generally represented by a.

How to find the given Sequence is A.P. or Not?

To find whether any given sequence is A.P. or Not, we can use the following steps:

Step 1: Find a_n.

Step 2: Find a_n+1 by replacing n with n+1 in a_n.

Step 3: Evaluate a_n+1 − a_n.

Step 4: If the result found in step 3 is independent of n then the sequence is an A.P. otherwise not an A.P.

Example: Show that the sequence defined by a_n = 4n − 1 is an A.P.

Solution:

Here, a_n = 4n − 1

Replace n with n+1 in a_n.

     a_n+1 = 4(n + 1) − 1

⇒  a_n+1 = 4n + 4 − 1

⇒  a_n+1 = 4n + 3

Now, calculate the value of a_n+1 − a_n.

      a_n+1 − a_n = 4n + 3 − (4n − 1)

⇒  a_n+1 − a_n  = 4n + 3 − 4n + 1

⇒   a_n+1 − a_n = 4

The value of a_n+1 − a_n is a constant value and it is independent of n.

Hence, the sequence a_n = 4n −1 is an A.P.

CBSE Class 10 Maths Notes Chapter 4 Arithmetic Progressions are an outstanding resource created by our team of knowledgeable Subject Experts at GfG. As ardent supporters of students’ education, we place a high priority on their learning and development, which is why we have written these in-depth notes to aid them in comprehending the challenging subject of arithmetic progressions.

Chapter 4 of the NCERT Class 10 Maths textbook finds the nth term of an arithmetic progression, summing the n terms of an arithmetic progression, calculating the arithmetic mean, and many other topics covered. These notes are intended to give students a thorough overview of the entire chapter, covering all the crucial topics, formulas, and ideas they will need to know to ace their examinations.