# CBSE Class 10 Maths Revision Notes Chapter 5

## Class 10 Mathematics Revision Notes for Arithmetic Progressions of Chapter 5

Mathematics is one of the most scoring subjects for Class 10 students. It is essential to thoroughly revise Class 10 Mathematics Chapter 5 Notes to perform well in examinations. Extramarks has provided the entire compilation of Class 10 Mathematics notes of Chapter 5 to help students understand concepts in a better way. Apart from Mathematics Chapter 5, notes of all other chapters are also available on Extramarks. These notes have been designed keeping the NCERT guidelines and CBSE syllabus into consideration. The study material is available in PDF format, which one can access from the official website.

Students can access the notes to get an idea about the important questions and topics covered in the examination. Chapter 5 Mathematics Class 10 Notes are created in simple language to make them easier for students to understand. Apart from the notes, students can access all the related study material such as formulas, CBSE question papers, answer keys, etc., from the Extramarks website.

## Access Class 10 Mathematics Chapter 5 – Arithmetic Progression Notes

### Definition of Arithmetic Progression:

• A sequence of numbers which we get by adding a fixed number to the preceding term starting from the first term such that the difference between each consecutive term remains the same.
• The fixed term is called the common difference of the arithmetic progression.
• The common difference can be positive, zero or negative.
• Each number in the list of arithmetic progressions is called a term.

### General term of an AP:

The general form of an arithmetic progression is:

a, a + d, a + 2d, a + 3d, ……….., a + (n -1)d

A.P. can be of two types. It is as follows:

Finite AP: A finite A.P. is one which has a finite number of terms with a + (n -1)d as the last term.

Example: 1, 3, 5, 7, ………,25

Infinite AP: An infinite A.P. is one which neither has a finite number of terms nor has the last term.

Example: 2,4,6,8……...∞

### Sum of the terms of an AP:

The sum of n terms of an A.P. if the first term and common difference is given:

S = n/2 (2a + (n -1) d)

The sum of n terms of an A.P. if the first term and last term l is given:

S = n/2 (a + l)

## Arithmetic Progression

### Common Difference

The difference between the two consecutive terms of an A.P. is known as the common difference.

For example: 3,6,9,12…….. The common difference here is 3.

Classification of the common differences:

• The common difference can be negative when the A.P. is decreasing.
• It can be positive when the A.P. is increasing.
• The common difference will be zero when the A.P. is constant.

### General Form of an Arithmetic Progression

The general form of an A.P. is (a, a + d, a + 2d, a + 3d……..) where a is considered the first term and d is the common difference. In the given condition, d = 0 OR d > 0 or d < 0.

### Finite and Infinite A.P.

Finite AP: An A.P. in which the number of terms is finite. Example: 2, 5, 8…….32, 38.

Infinite AP: An A.P. in which there are an infinite number of terms. Example: 2, 4, 6, 7, 9……

### Sum of Arithmetic Progressions

The sum of n terms of an A.P. with a as its first term and d as a common difference is written as:

Sn = n/2 (2a + (n-1)d)

### Arithmetic Mean

The arithmetic mean is the average of a given set of numbers. It is calculated as:

AM = Sum of terms/Number of terms

For example: if x, y and z are in arithmetic progression, then their mean will be y = (x + z)/2. Here, y is the arithmetic mean of x and z.

### Properties of Arithmetic Progressions

• If the same number is added or subtracted from each A.P. term, the resulting terms are also in A.P. with the identical common difference.
• If each term in A.P. is divided or multiplied by the same non-zero number, then the resulting series will also be in A.P.
• The three numbers x, y and z  will be an A.P. when 2y = x + z.
• If the nth term of a series is a linear expression, then the series is an A.P.
• If we choose terms from the A.P. in a regular interval, the chosen terms will also constitute an A.P.
• If the terms of an A.P. are increased or decreased with the same amount,  the resulting sequence will also be an A.P.

### Solved Examples

Example 1:

For the AP: 3/2, 1/2, -½, -3/2, …..  write the first term a and the common difference d.

Solution:

Here a = 3/2, d = 1

Example 2:

Find the 10th term of the AP: 2, 7, 12, …..

Solution:

Here, a = 2, d = 7-2 = 5 and n = 10.

We have an = a + (n – 1)d

So a10 = 2 + (10 – 1) X 5 = 2 + 45 = 47

Example 3:

Find the sum of the first 22 terms of the AP: 8, 3, -2, …..

Here, a = 8, d = 3 – 8 = –5, and n = 22.

Since, S = n/2 [2a + (n – 1)d]

Therefore, S = 22/2 [16 + 21 (-5)] = 11 (16 – 105) = 11(-89) = -979

Hence the sum of the first 22 terms of the A.P. will be – 979.

### Important Points on Arithmetic Progression

• If each term in the A.P. is increased, decreased, multiplied, or divided by the same non-zero constant, then the following sequence will be in A.P.
• In the A.P., all the terms that are equidistant from the start to end will be constant.
• To solve most of the problems related to A.P., the terms can be taken as:

3 terms: (a – d), a, (a + d)

4 terms: (a – 3d), (a – d), (a + d), (a + 3d)

### Important formulas in AP

 First term of AP a, a + d, a + 2d, a + 3d, a + 4d, …………, a + (n – 1)d Common Difference in AP d = a2 – a1 = a3 – a2 = ………..= an – an – 1 nth term of an AP an = a + (n -1) x d Sum of N terms of AP Sn = n/2 (2a + (n – 1) d)

## FAQs (Frequently Asked Questions)

### 1. How many exercises are there in Class 10 Mathematics Chapter 5?

There are a total of 4 exercises in the NCERT book Class 10 Mathematics Chapter 5. All the questions are designed by experts according to the CBSE guidelines. Students should practice the problems given in the book for board exam preparation.

### 2. Where can I get Class 10 Chapter 5 Mathematics notes?

Students can access the Chapter 5 Mathematics Class 10 Notes from the website of Extramarks. The notes contain detailed information related to arithmetic progressions that will help students understand the basic and advanced concepts easily. In addition, candidates can also find study materials such as CBSE sample papers, CBSE past years’ question papers, etc., from Extramarks to prepare for the examination.

### 3. Why should I study Mathematics Chapter 5 of Class 10?

Arithmetic progressions is an important chapter in terms of both exam preparation and practical application. It is taught in higher classes as well, so candidates should study it thoroughly to establish a solid foundation. One can access and refer to the essential study material, such as CBSE extra questions, notes, etc., available on the Extramarks website.