NCERT Solutions for Class 10 Maths Chapter 5 AP Arithmetic Progression

Updated on January 7, 2025
by Tiwari Academy

NCERT Detailed Solutions for Class 10 Maths Chapter 5 AP Arithmetic Progression in English and Hindi Medium CBSE Session 2025-26. Class 10 NCERT Math textbook Chapter 5 Exercises are according to CBSE Mathematics books published 2025-26 Exams. NCERT Detailed Solutions for Class 10 Mathematics Chapter 5, Arithmetic Progressions (AP), are essential for students aiming to build a solid foundation in this concept. NCERT 10th Math chapter 5 covers the basics of sequences, focusing on understanding how numbers form a progression. Grade 10th NCERT Textbook Maths Exercise 5 solutions explain key topics such as the general form of an AP, the nth term formula and the sum of n terms in detail.

Students can use these solutions to solve Class 10 NCERT Math Chapter 5 exercise problems, such as finding the common difference or determining whether a sequence qualifies as an AP. Downloadable PDFs for Class 10 NCERT Book Mathematics Chapter 5 Exercise solutions allow students to study offline. By practicing solved examples and working through Class 10 Math Chapter 5 practice questions, students can develop confidence for exams. These solutions also address previous year questions and MCQs that frequently appear in the board exams.

The Arithmetic Progressions Class 10 NCERT Math Solutions also focus on improving problem-solving skills through detailed step-by-step explanations. For instance, students learn how to derive the nth term of an AP, calculate the sum of n terms and analyze patterns using Arithmetic Progression formulas in NCERT 10th Mathematics. These NCERT Textbook Class 10 Maths Chapter 5 Exercises solutions not only clarify difficult concepts but also provide video solutions to guide students visually.

Worksheets and assignments included with these solutions help students practice regularly and reinforce their understanding of Class 10 Maths NCERT Book Chapter 5 notes. For those preparing for competitive exams or seeking additional support, the solutions provide questions based on NCERT Exercise Class 10 Maths Chapter 5 important topics. Solving these problems builds accuracy and the PDF solutions are particularly useful for last-minute revisions before exams.

Chapter 1 Real Numbers Important Questions
Chapter 2 Polynomials Important Questions
Chapter 3 Linear Equations Important Questions
Chapter 4 Quadratic Equations Important Questions
Chapter 5 Arithmetic Progression Important Questions
Chapter 6 Triangles Important Questions
Chapter 7 Coordinate Geometry Important Questions
Chapter 8 Introduction to Trigonometry Important Questions
Chapter 9 Application of Trigonometry Important Questions
Chapter 10 Circles Important Questions
Chapter 11 Areas Related to Circles Important Questions
Chapter 12 Surface Areas and Volumes Important Questions
Chapter 14 Probability Important Questions

Key Points to Remember in Class 10 Maths Chapter 5 for Board Exams

Class 10 Maths Chapter 5, Arithmetic Progressions, focuses on key concepts like the nth term formula (𝑎𝑛 = 𝑎 + (𝑛 − 1)𝑑), the sum of n terms formula Sn = n/2[2a+(n−1)d]), identifying AP sequences, solving word problems and understanding real-life applications. These are crucial for board exam preparation.

Day Topics to Cover Practice Revision Tasks
Day 1 Introduction to Arithmetic Progressions (AP), nth term formula Solve basic examples from NCERT textbook
Day 2 Sum of n terms formula and its derivation Practice NCERT exercise problems on sum of n terms
Day 3 Identifying AP sequences and solving real-life word problems Attempt examples and miscellaneous exercise from NCERT
Day 4 Review and revise key formulas and concepts Solve previous year board exam questions on AP
Day 5 Take a mock test on Chapter 5 (AP) Analyze mistakes and focus on weak areas

NCERT Class 10 Mathematics Chapter 5 solutions are designed to help students excel in CBSE board exams by addressing frequently asked questions and high-weightage topics. The NCERT Textbook Class 10 Math Chapter 5 Complete explanations simplify complex concepts, making them easy to understand even for beginners. Students can work on Arithmetic Progression problems using NCERT Book solved examples, practice tests and worksheets, all of which are available in the PDF format.

Grade 10th Mathematics Chapter 5 solutions also include a summary of Class 10 Maths Chapter 5 Exercises, offering a quick revision tool before exams. By practicing Class 10th NCERT Math Book Chapter 5 MCQ and CBSE previous year questions, students can familiarize themselves with the exam pattern and scoring criteria. The availability of online tests and video solutions further enhances their preparation, ensuring they gain mastery over the Arithmetic Progression concepts in CBSE Class 10 Mathematics.

Class 10 Maths Chapter 5 Topics
Class: 10Mathematics
Chapter 5:Arithmetic Progression
Content:Exercise Questions Solutions
Content Format:Text, Images, PDF and Videos
Academic Session:Year 2025-26
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, and other state boards 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 Simplified solutions are based on latest NCERT Books. These apps are applicable for UP Board (Higher Secondary) with CBSE Board and other boards who are using NCERT Books 2025-26 in Hindi and English medium. Download Class 10 Maths Apps based on updated NCERT Solutions for new academic session 2025-26.

10th Maths Chapter 5 Solutions

NCERT Solutions for class 10 Maths chapter 5 all exercises are given to free use. NCERT Solutions 2025-26 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.

Class 10 Maths Chapter 5 Solutions

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.

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.

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?

To practice Arithmetic Progression in Class 10 Maths, start by understanding the formulas for the nth term and the sum of n terms. Solve NCERT textbook exercises, including examples and miscellaneous problems. Practice previous year board questions and MCQ. Use worksheets for additional practice and attempt mock tests to strengthen your problem-solving skills and speed.

Step 1: Learn class 10 Maths chpater 5 with basics and Examples before starting.

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.

Step 2: To solve sums of 10th Maths chpater 5 take help from Online Learning Platform. The NCERT Textbook 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.

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.

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.

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.

What topics are covered in NCERT Solutions for Class 10 Maths Chapter 5?

NCERT PDF Solutions for Class 10 Mathematics Chapter 5, Arithmetic Progressions, cover a range of topics essential for understanding sequences. These include the definition of an AP, the formula for finding the nth term and methods to calculate the sum of n terms. The solutions also include step-by-step explanations for exercise questions, NCERT Book solved examples and conceptual clarifications. The chapter addresses application-based problems, such as finding missing terms in a sequence or verifying if a series forms an AP. These topics are designed to help students master the concept of Arithmetic Progression effectively.

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.

Are the NCERT Solutions for Arithmetic Progressions useful for board exams?

Yes, the NCERT Textbook Solutions for Arithmetic Progressions are extremely useful for board exams. They provide detailed solutions to textbook exercises and cover important questions that frequently appear in exams. These solutions are structured to help students understand how to approach problems logically and systematically. They also include practice questions, Multiple Choice Questions and examples that align with the CBSE syllabus. Solving these problems ensures that students are well-prepared for the board exam and gain confidence in tackling AP-related questions, which carry significant weight in the Class 10 Mathematics exam.

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.

How can I download Class 10 Maths Chapter 5 solutions in PDF format?

Class 10 Maths Chapter 5 solutions are available for download in PDF format on various educational websites (like Tiwari Academy) and apps (as Tiwari Academy Learning App). These PDFs are designed to be user-friendly and include all exercise solutions, notes and summaries for the chapter. Simply search for Class 10 Maths Chapter 5 NCERT Simple Solutions PDF download and you will find several reliable platforms offering free or subscription-based downloads. Having these solutions offline allows students to study anytime and refer to the solved examples, previous year questions and Arithmetic Progression formulas without needing constant internet access.

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.

What additional resources can I use to practice Class 10 Maths Chapter 5?

In addition to NCERT Solutions, students can practice Class 10 Maths Chapter 5 using online quizzes, practice tests and worksheets available on educational platforms. These resources often include challenging questions based on Arithmetic Progression formulas and application-based problems. Video tutorials and step-by-step video solutions are also helpful for visual learners. Many platforms provide assignments, notes and summaries tailored to CBSE exam patterns, ensuring students gain a deeper understanding of the topic. By combining textbook exercises with additional resources, students can enhance their preparation and score better in exams.

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.

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Last Edited: January 7, 2025
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Content Reviewed: January 7, 2025
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