# NCERT Solutions for Class 10 Maths Chapter 5

NCERT solutions for class 10 Maths chapter 5 all exercises of AP – Arithmetic Progression updated for new academic session 2021-2022. These solutions are useful for not only for CBSE Board but UP Board, MP Board, Gujrat Board, etc. also who are using NCERT Textbooks as a course books. Uttar Pradesh Madhyamik Shiksha parishad, Prayagraj has implemented NCERT Books for Class 10 students. So, UP Board High school students can download UP Board Solutions for Class 10 Maths Chapter 5 in Hindi and English Medium here. All the Online and Offline Apps, NCERT solutions are based on latest NCERT Books 2021-2022.

These apps are applicable for UP Board (Higher Secondary) with CBSE Board and other boards who are using NCERT Books 2021-22 in Hindi and English medium. Download Class 10 Maths Apps based on updated NCERT Solutions for new academic session 2021-22.## Class 10 Maths chapter 5 Arithmetic Progression – AP Solution

### 10th Maths Chapter 5 Exercise 5.1

### 10th Maths Chapter 5 Exercise 5.2

### 10th Maths Chapter 5 Exercise 5.3

### 10th Maths Chapter 5 Exercise 5.4

Class: 10 | Maths (English and Hindi Medium) |

Chapter 5: | Arithmetic Progression |

### 10th Maths Chapter 5 Solutions

NCERT Solutions for class 10 Maths chapter 5 all exercises are given to free use. NCERT Solutions 2021-22 and NCERT books are in PDF format to study online/offline by downloading in your device. Go through this page completely to know more about arithmetic series. Be connected with us to get the latest update regarding to CBSE solutions, Sample Papers, board questions and all other study material related to class 10 Maths solutions of AP.

#### Class 10 Maths Chapter 5 Solution in Hindi Medium Videos

#### Class 10 Maths Chapter 5 Exercise 5.1 Solution in Videos

#### Class 10 Maths Chapter 5 Exercise 5.2 Solution in Videos

#### Class 10 Maths Chapter 5 Exercise 5.3 Solution in Videos

#### Class 10 Maths Chapter 5 Exercise 5.4 Solution in Videos

### NCERT Solutions for Class 10 Maths Chapter 5

- NCERT Solutions 10th MathsExercise 5.1Read more
- NCERT Solutions 10th MathsExercise 5.2Read more
- NCERT Solutions 10th MathsExercise 5.3Read more
- NCERT Solutions 10th MathsExercise 5.4Read more

### Extra Questions on 10th Maths Chapter 5?

##### What is an Arithmetic Progression (AP)?

An arithmetic progression (AP) is a list (or pattern or series) of numbers in which each next term is obtained by adding or subtracting a fixed number to the preceding term except the first term. This fixed number is called the common difference of the AP, it may be positive, negative or zero.

##### What are the objective of studying Arithmetic Progression?

Objective of studying Arithmetic Progression – AP

To identify arithmetic progression from a given list of numbers, to determine the general term of an arithmetic progression and to find the sum of first n terms of an arithmetic progression.

##### What is general form of Arithmetic Progression?

a, a + d, a + 2d, a + 3d, . . . is the general form of Arithmetic Progression where a is first term and d is common difference.

#### Previous Years Questions

TWO MARKS QUESTIONS

1. Find how many integers between 200 and 500 are divisible by 8. [CBSE 2017]

THREE MARKS QUESTIONS

1. Find the sum of n terms of the series (4 – 1/n) + (4 – 2/n) + (4 – 3/n) + …. [CBSE 2017]

2. If the mth term of an AP is 1/n and nth term is 1/m then show that its (mn)th term is 1. [CBSE 2017]

FOUR MARKS QUESTIONS

1. If the sum of first m terms of an A. P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero. [CBSE 2017]

2. The ratio of the sums of first m and first n terms of an AP is m2:n2. Show that the ratio of its mth and nth terms is (2m – 1):(2n – 1). [CBSE 2017]

##### About Arithmetic Progression – AP

- a, a + d, a + 2d, a + 3d, . . . is called the general form of an AP, where a is the first term and d the common difference. If there are a finite number of terms in the AP, then it is called a finite AP.
- The general formula for finding nth term is given by a + (n-1)d and the sum of n terms is given by n/2[2a + (n-1)d]. The last term is denoted by l and given by a + (n-1)d.

###### Historical Facts!

- Leonardo Pisano Bigollo also known as Leonardo of Pisano, Leonardo Bonacci, Leonardo Fibonacci was an Italian mathematician. He gave Fibonacci series on the basis of, how fast rabbits could breed in ideal circumstances. Fibonacci Series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … Here, every next term is sum of previous two terms. For the solutions of other maths chapters of class 10, click here.
- Once, when famous mathematician Carl Friedrich Gauss (1777 – 1855) misbehaved in primary school, his teacher I.G. Buttner gave him a task to add a list of integers from 1 to 100. Gauss’s method was to realise that pairwise addition of terms from opposite ends of the list yielded identical intermediate sum: 1 + 100 = 2 + 99 = 3 + 98 = … = 50 + 51 = 101. So, here 1 + 2+ 3 + 4 + …. + 100 = the sum of 50 sums each equal to 101. Therefore, the sum is 5050. Finally he gave the answer in seconds.

##### Which exercise of 10th Maths chapter 5 need less efforts?

Class 10th Maths exercise 5.2 and 5.3 are easier to solve and the scoring also. The questions given in these two exercise are based on just to formulae – nth term and sum to n terms. Most of the questions get solved just by putting the values in proper formula. So, a student can score more easily in these two exercises.

##### How many exercises are there in 10th Maths Chapter 5 AP?

There are 4 exercises in chapter 4 of class 10 Maths subject. Out of these exercise 5.4 is an optional exercise, which is not important for examination point of view. It is given just to practice and enhance the knowledge in arithmetic progression.

##### Is chapter 5 Arithmetic Progression of 10th Maths interesting?

Yes, chapter 5 of 10th Maths is very interesting chapter because you can observe Arithmetic Progressions around you at various points.

Examples of AP around you: 1) The heights (in cm) of some students of a school standing in a queue in the morning assembly are 147, 148, 149, . . ., 157.

2) The cash prizes (in Rs) given by a school to the toppers of Classes I to XII are, respectively, 200, 250, 300, 350, . . ., 750.

##### Is there any optional exercise in chapter 5 Class 10th Math?

Yes, there is optional exercise in chapter 5 of 10th Maths. Fourth exercise (exercise 5.4) is the optional exercise. Exercise 5.4 is not an easy exercise because this exercise contains very tricky questions.

##### Why chapter 5 of 10th Math important?

Chapter 5 (Arithmetic Progression) of 10th Math is important because students have to study Arithmetic Progression in class 11 maths also. Arithmetic Progression(chapter 5) of 10th maths is base of Arithmetic Progression of class 11th maths.