 NCERT solutions for class 10 Maths chapter 5 all exercises of AP Arithmetic Progression in Hindi and English Medium updated for new academic session 2023-24. Class 10 Maths solution is updated according to new textbooks published for CBSE 2023-24 exams.

• ## 10th Maths Chapter 5 Exercise 5.1 Solutions

• ### 10th Maths Chapter 5 Exercise 5.4 Solutions Class: 10 Mathematics Chapter 5: Arithmetic Progression Content: Exercise Questions Solutions Content Format: Text, Images, PDF and Videos Academic Session: Year 2023-24 Medium Type: English and Hindi Medium

### Class 10 Maths chapter 5 Arithmetic Progression – AP Solution

Class 10 Maths Chapter 5 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 2023-24. These apps are applicable for UP Board (Higher Secondary) with CBSE Board and other boards who are using NCERT Books 2023-24 in Hindi and English medium. Download Class 10 Maths Apps based on updated NCERT Solutions for new academic session 2023-24.

### 10th Maths Chapter 5 Solutions

NCERT Solutions for class 10 Maths chapter 5 all exercises are given to free use. NCERT Solutions 2023-24 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. ### 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.

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#### Previous Years Questions

TWO MARKS QUESTIONS
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!

1. 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.
2. 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.

### How to Practice Arithmetic Progression in Class 10 Maths?

We all know the current state of education infrastructure of the country after the COVID-19 impact. We say education is evolving from Didactic methodology to concept-based education. However, it is still very expensive for most of the students to gain access. The disproportionate effects of the COVID-19 pandemic affected brilliant and average minds also. Undoubtedly, students and teachers are sailing the same boat to make the preparations effective. Some of the students are still finding ways to score 100% in the Maths board exam for 10th grade. We selected some of the suggestions that can help you to score well in Chapter 4 AP of class 10th.

#### Step 1: Learn class 10 Maths chpater 5 with basics and Examples before starting. Class 10 Maths Chapter 5 solutions is important for higher classes also. Many scholars consider high school Maths is the origin of many main subjects in senior school, which directly- indirectly affects the performance in upcoming classes. Unlike language, mathematics has set of rules which don’t let examiners deduct marks. So many students with a firm understanding of formulae and dedication can easily score 100% on Class X boards. Start by following the NCERT book’s chapter explanations. This is a small step towards developing the skills to solve problems without being anxious. Being panicked will scare you with Maths, not good if you want to improve.

#### Step 2: To solve sums of 10th Maths chpater 5 take help from Online Learning Platform. The NCERT Solutions for Class 10 Maths chapter 5 helps the students in learning online also. Choosing the right study style that works for you is important. Take help from online learning platforms. The best thing about e-learning is that it is flexible. Every student has different ways to retain information. Some prefer reading and learning whereas some want more visual, audio, or kinetic forms of learning. Online you will find many such explanations that work for you, but choosing among them is a challenge or some are costly for you. At Tiwari Academy, you will get tailored explanations in form of audio, videos, and PDF for which you don’t have to pay subscriptions. Our step toward democratized education to all who wish to pursue Excellency.

#### Step 3: Class 10 Maths chapter 5 needs regular Homework and revision session. Get good practice in 10th Maths chapter 5 by revision and practice. Homework are the revision of what you have learned in the class. Give it some time post classes to write. This is called making notes, summarization will help you with your homework. This way you will come up with doubts, which you can clear in the next lectures. Writing the concept when you learn fresh will help you to retain it. Keep this notebook separate. It will help you to when you will deeply study or during revision. We also suggest you to complete the skimming of the chapter and examples before classroom discussions so that you can clear your doubts easily.

#### Step 4: Once go through the chapter 5 NCERT 10th Maths before it starts in the class. Avoid Brain dump. We understand throughout class you can focus for a limited time. Meanwhile, teachers cramping down the information that you are not going to retain anyway. While preparing the chapter in small chunks will help you to recall the information. Psychologists consider it a cognitive way of learning effectively to improve the Maths skill. Participating or teaching your peers is another form of learning because this way you will use the knowledge that you gained. Also, you will teach them and listen too, what they are saying, will help you.

#### Step 5: Be confident with the help of regular practice in AP. Practice in writing skills are entangled with critical thinking. It also has involvement for performance in all areas of school curriculum and examinations. By writing the answer in exams, we express what we have learned. So, if you know every step to solve the equations of Arithmetic Progression and practice it well, definitely you will be confident in exams. Just because of confidence, you will be able to achieve 100% marks. Maths is a series of chapters and ideas, concepts that are interlinked with each other. Instead, try to explore the other ways to solve the questions by understanding the importance and how to imply the concepts. If you want to know about the alternate ways of solving the problems, just check the videos’ explanations of Arithmetic progression on Tiwari Academy website.

### 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.

Last Edited: August 26, 2023