Open App

Class 10 Exam > Class 10 Notes > Mathematics Class 10 (Maharashtra SSC Board) > Textbook Solutions: Arithmetic Progression

Textbook Solutions: Arithmetic Progression | Mathematics Class 10 (Maharashtra SSC Board) PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


Arithmetic Progression 
 
 
Practice Set 3.1 
Q. 1 A. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
2, 4, 6, 8, . . . 
Answer : 
2, 4, 6, 8, . . . 
Here, the first term, a1 = 2 
Second term, a2 = 4 
a3 = 6 
Now, common difference = a2 – a1 = 4 – 2 = 2 
Also, a3 – a2 = 6 – 4 = 2 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 2. 
Q. 1 B. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
 
Answer : 
 
Here, the first term, a1 = 2 
Page 2


Arithmetic Progression 
 
 
Practice Set 3.1 
Q. 1 A. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
2, 4, 6, 8, . . . 
Answer : 
2, 4, 6, 8, . . . 
Here, the first term, a1 = 2 
Second term, a2 = 4 
a3 = 6 
Now, common difference = a2 – a1 = 4 – 2 = 2 
Also, a3 – a2 = 6 – 4 = 2 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 2. 
Q. 1 B. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
 
Answer : 
 
Here, the first term, a1 = 2 
 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, ?? =
1
2
 . 
Q. 1 C. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
– 10, – 6, – 2, 2, . . . 
Answer : 
– 10, – 6, – 2,2, . . . 
Here, the first term, a1 = – 10 
Second term, a2 = – 6 
a3 = – 2 
Now, common difference = a2 – a1 = – 6 – ( – 10) = – 6 + 10 = 4 
Also, a3 – a2 = – 2 – ( – 6) = – 2 + 6 = 4 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 4. 
Q. 1 D. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
0.3, 0.33, .0333, . . . 
Page 3


Arithmetic Progression 
 
 
Practice Set 3.1 
Q. 1 A. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
2, 4, 6, 8, . . . 
Answer : 
2, 4, 6, 8, . . . 
Here, the first term, a1 = 2 
Second term, a2 = 4 
a3 = 6 
Now, common difference = a2 – a1 = 4 – 2 = 2 
Also, a3 – a2 = 6 – 4 = 2 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 2. 
Q. 1 B. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
 
Answer : 
 
Here, the first term, a1 = 2 
 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, ?? =
1
2
 . 
Q. 1 C. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
– 10, – 6, – 2, 2, . . . 
Answer : 
– 10, – 6, – 2,2, . . . 
Here, the first term, a1 = – 10 
Second term, a2 = – 6 
a3 = – 2 
Now, common difference = a2 – a1 = – 6 – ( – 10) = – 6 + 10 = 4 
Also, a3 – a2 = – 2 – ( – 6) = – 2 + 6 = 4 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 4. 
Q. 1 D. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
0.3, 0.33, .0333, . . . 
Answer : 
0.3, 0.33, 0.333,….. 
Here, the first term, a1 = 0.3 
Second term, a2 = 0.33 
a3 = 0.333 
Now, common difference = a2 – a1 = 0.33 – 0.3 = 0.03 
Also, a3 – a2 = 0.333 – 0.33 = 0.003 
Since, the common difference is not same. 
Hence the terms are not in Arithmetic progression 
Q. 1 E. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
0, – 4, – 8, – 12, . . . 
Answer : 
0, – 4, – 8, – 12, . . . 
Here, the first term, a1 = 0 
Second term, a2 = – 4 
a3 = – 8 
Now, common difference = a2 – a1 = – 4 – 0 = – 4 
Also, a3 – a2 = – 8 – ( – 4) = – 8 + 4 = – 4 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = – 4. 
Q. 1 F. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
Page 4


Arithmetic Progression 
 
 
Practice Set 3.1 
Q. 1 A. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
2, 4, 6, 8, . . . 
Answer : 
2, 4, 6, 8, . . . 
Here, the first term, a1 = 2 
Second term, a2 = 4 
a3 = 6 
Now, common difference = a2 – a1 = 4 – 2 = 2 
Also, a3 – a2 = 6 – 4 = 2 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 2. 
Q. 1 B. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
 
Answer : 
 
Here, the first term, a1 = 2 
 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, ?? =
1
2
 . 
Q. 1 C. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
– 10, – 6, – 2, 2, . . . 
Answer : 
– 10, – 6, – 2,2, . . . 
Here, the first term, a1 = – 10 
Second term, a2 = – 6 
a3 = – 2 
Now, common difference = a2 – a1 = – 6 – ( – 10) = – 6 + 10 = 4 
Also, a3 – a2 = – 2 – ( – 6) = – 2 + 6 = 4 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 4. 
Q. 1 D. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
0.3, 0.33, .0333, . . . 
Answer : 
0.3, 0.33, 0.333,….. 
Here, the first term, a1 = 0.3 
Second term, a2 = 0.33 
a3 = 0.333 
Now, common difference = a2 – a1 = 0.33 – 0.3 = 0.03 
Also, a3 – a2 = 0.333 – 0.33 = 0.003 
Since, the common difference is not same. 
Hence the terms are not in Arithmetic progression 
Q. 1 E. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
0, – 4, – 8, – 12, . . . 
Answer : 
0, – 4, – 8, – 12, . . . 
Here, the first term, a1 = 0 
Second term, a2 = – 4 
a3 = – 8 
Now, common difference = a2 – a1 = – 4 – 0 = – 4 
Also, a3 – a2 = – 8 – ( – 4) = – 8 + 4 = – 4 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = – 4. 
Q. 1 F. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
Answer : 
 
 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, ?? = 0. 
Q. 1 G. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
 
Answer : 
3, 3 + v2, 3 + 2v2, 3 + 3v2, …. 
Here, the first term, a1 = 3 
Second term, a2 = 3 + v2 
Page 5


Arithmetic Progression 
 
 
Practice Set 3.1 
Q. 1 A. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
2, 4, 6, 8, . . . 
Answer : 
2, 4, 6, 8, . . . 
Here, the first term, a1 = 2 
Second term, a2 = 4 
a3 = 6 
Now, common difference = a2 – a1 = 4 – 2 = 2 
Also, a3 – a2 = 6 – 4 = 2 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 2. 
Q. 1 B. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
 
Answer : 
 
Here, the first term, a1 = 2 
 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, ?? =
1
2
 . 
Q. 1 C. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
– 10, – 6, – 2, 2, . . . 
Answer : 
– 10, – 6, – 2,2, . . . 
Here, the first term, a1 = – 10 
Second term, a2 = – 6 
a3 = – 2 
Now, common difference = a2 – a1 = – 6 – ( – 10) = – 6 + 10 = 4 
Also, a3 – a2 = – 2 – ( – 6) = – 2 + 6 = 4 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 4. 
Q. 1 D. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
0.3, 0.33, .0333, . . . 
Answer : 
0.3, 0.33, 0.333,….. 
Here, the first term, a1 = 0.3 
Second term, a2 = 0.33 
a3 = 0.333 
Now, common difference = a2 – a1 = 0.33 – 0.3 = 0.03 
Also, a3 – a2 = 0.333 – 0.33 = 0.003 
Since, the common difference is not same. 
Hence the terms are not in Arithmetic progression 
Q. 1 E. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
0, – 4, – 8, – 12, . . . 
Answer : 
0, – 4, – 8, – 12, . . . 
Here, the first term, a1 = 0 
Second term, a2 = – 4 
a3 = – 8 
Now, common difference = a2 – a1 = – 4 – 0 = – 4 
Also, a3 – a2 = – 8 – ( – 4) = – 8 + 4 = – 4 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = – 4. 
Q. 1 F. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
Answer : 
 
 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, ?? = 0. 
Q. 1 G. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
 
Answer : 
3, 3 + v2, 3 + 2v2, 3 + 3v2, …. 
Here, the first term, a1 = 3 
Second term, a2 = 3 + v2 
a3 = 3 + 2v2 
Now, common difference = a2 – a1 = 3 + v2 – 3 = v2 
Also, a3 – a2 = 3 + 2v2 –(3 + v2) = 3 + 2v2 – 3 – v2 = v2 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = v2 . 
Q. 1 H. Which of the following sequences are A.P. ? If they are A.P. find the 
common difference. 
 
127, 132, 137, . . . 
Answer : 127, 132, 137, . . . 
Here, the first term, a1 = 127 
Second term, a2 = 132 
a3 = 137 
Now, common difference = a2 – a1 = 132 – 127 = 5 
Also, a3 – a2 = 137 – 132 = 5 
Since, the common difference is same. 
Hence the terms are in Arithmetic progression with common difference, d = 5. 
Q. 2 A. Write an A.P. whose first term is a and common difference is d in each of 
the following. 
 
a = 10, d = 5 
Answer : a = 10, d = 5 
Let a1 = a = 10 
Since, the common difference d = 5 
Using formula an + 1 = an + d 
Thus, a2 = a1 + d = 10 + 5 = 15

	Mathematics Class 10 (Maharashtra SSC Board) 26 videos\|208 docs\|38 tests

Mathematics Class 10 (Maharashtra SSC Board)

26 videos|208 docs|38 tests

Join Course for Free

FAQs on Textbook Solutions: Arithmetic Progression - Mathematics Class 10 (Maharashtra SSC Board)

1. What is an arithmetic progression and how is it defined?

Ans.An arithmetic progression (AP) is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is known as the common difference. An AP can be expressed in the form a, a + d, a + 2d, ..., where 'a' is the first term and 'd' is the common difference.

2. How do you find the nth term of an arithmetic progression?

Ans.The nth term of an arithmetic progression can be calculated using the formula: nth term = a + (n - 1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number you want to find.

3. What is the formula for the sum of the first n terms of an arithmetic progression?

Ans.The sum of the first n terms (S_n) of an arithmetic progression can be found using the formula: S_n = n/2 * (2a + (n - 1)d) or alternatively S_n = n/2 * (first term + last term). Here, 'n' is the number of terms, 'a' is the first term, and 'd' is the common difference.

4. Can you give an example of an arithmetic progression with its common difference?

Ans.An example of an arithmetic progression is 3, 7, 11, 15, 19. In this sequence, the common difference is 4, as each term increases by 4 from the previous term.

5. How is the concept of arithmetic progression applied in real life?

Ans.Arithmetic progression is used in various real-life scenarios, such as calculating the total cost of items that increase by a fixed amount, determining schedules, and in financial calculations like amortization where payments occur at regular intervals.

About this Document

4.64/5 Rating

Sep 23, 2025 Last updated

Related Exams

Class 10

Document Description: Textbook Solutions: Arithmetic Progression for Class 10 2025 is part of Mathematics Class 10 (Maharashtra SSC Board) preparation. The notes and questions for Textbook Solutions: Arithmetic Progression have been prepared according to the Class 10 exam syllabus. Information about Textbook Solutions: Arithmetic Progression covers topics like and Textbook Solutions: Arithmetic Progression Example, for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Textbook Solutions: Arithmetic Progression.

Introduction of Textbook Solutions: Arithmetic Progression in English is available as part of our Mathematics Class 10 (Maharashtra SSC Board) for Class 10 & Textbook Solutions: Arithmetic Progression in Hindi for Mathematics Class 10 (Maharashtra SSC Board) course. Download more important topics related with notes, lectures and mock test series for Class 10 Exam by signing up for free. Class 10: Textbook Solutions: Arithmetic Progression | Mathematics Class 10 (Maharashtra SSC Board)

Description

Full syllabus notes, lecture & questions for Textbook Solutions: Arithmetic Progression | Mathematics Class 10 (Maharashtra SSC Board) - Class 10 | Plus excerises question with solution to help you revise complete syllabus for Mathematics Class 10 (Maharashtra SSC Board) | Best notes, free PDF download

Information about Textbook Solutions: Arithmetic Progression

In this doc you can find the meaning of Textbook Solutions: Arithmetic Progression defined & explained in the simplest way possible. Besides explaining types of Textbook Solutions: Arithmetic Progression theory, EduRev gives you an ample number of questions to practice Textbook Solutions: Arithmetic Progression tests, examples and also practice Class 10 tests

	Mathematics Class 10 (Maharashtra SSC Board) 26 videos\|208 docs\|38 tests

Mathematics Class 10 (Maharashtra SSC Board)

26 videos|208 docs|38 tests

Join Course for Free

Download as PDF

Explore Courses for Class 10 exam

study material

MCQs

shortcuts and tricks

Free

Sample Paper

Textbook Solutions: Arithmetic Progression | Mathematics Class 10 (Maharashtra SSC Board)

Extra Questions

mock tests for examination

practice quizzes

Textbook Solutions: Arithmetic Progression | Mathematics Class 10 (Maharashtra SSC Board)

pdf

Important questions

Textbook Solutions: Arithmetic Progression | Mathematics Class 10 (Maharashtra SSC Board)

Objective type Questions

Viva Questions

Summary

Previous Year Questions with Solutions

Semester Notes

past year papers

Exam

video lectures

ppt

;

Additional Information about Textbook Solutions: Arithmetic Progression for Class 10 Preparation

Textbook Solutions: Arithmetic Progression Free PDF Download

The Textbook Solutions: Arithmetic Progression is an invaluable resource that delves deep into the core of the Class 10 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the Textbook Solutions: Arithmetic Progression now and kickstart your journey towards success in the Class 10 exam.

Importance of Textbook Solutions: Arithmetic Progression

The importance of Textbook Solutions: Arithmetic Progression cannot be overstated, especially for Class 10 aspirants. This document holds the key to success in the Class 10 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Textbook Solutions: Arithmetic Progression Notes

Textbook Solutions: Arithmetic Progression Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Textbook Solutions: Arithmetic Progression. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Textbook Solutions: Arithmetic Progression Notes on EduRev are your ultimate resource for success.

Textbook Solutions: Arithmetic Progression Class 10 Questions

The "Textbook Solutions: Arithmetic Progression Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Textbook Solutions: Arithmetic Progression on the App

Students of Class 10 can study Textbook Solutions: Arithmetic Progression alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Textbook Solutions: Arithmetic Progression, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Textbook Solutions: Arithmetic Progression is prepared as per the latest Class 10 syllabus.

Education Revolution