NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progression Exercise 5.1

NCERT books are regarded as vital texts whose advantages would aid in laying the groundwork for academic or competitive examinations for CBSE students. NCERT books are incredibly beneficial for students since they give them a solid foundation and expand their knowledge. NCERT books are more than sufficient to cover and advance the comprehension of essential concepts in every subject in a condensed and simple style. One significant benefit of using NCERT books is that they help students understand topics. Instead of just memorising topics, students must concentrate on understanding them. When students comprehend the material, any inquiry about that subject may be answered with ease. The NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will help students to understand the complex and complicated topics of the NCERT books and more. Students will be able to solve any question with the help of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1. The NCERT Solutions For Class 10 Maths Subject 5 Exercise 5.1 will aid students in comprehending even the challenging and complex concepts in the chapter. Students will be able to answer the challenging questions in NCERT Solutions For Class 10 Maths Subject 5 Exercise 5.1. Although students may perceive Mathematics to be a challenging subject, NCERT books have been written in straightforward language. When students struggle to grasp NCERT exercise questions, getting NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 from Extramarks’ website is the quickest and clearest option to address the issues.

Students must concentrate on the patterns presented in the NCERT books to avoid becoming perplexed during the examination.A student with a sharp understanding of questions can easily solve any question that will be asked in examinations. Hence, it is important to know the pattern of NCERT books and study it minutely with the help of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1. Here, students studying for the CBSE Class 10 Mathematics examinations can access NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 Arithmetic Progression. To perform well in the Class 10 examination, the students must become familiar with these NCERT solutions. The experts at Extramarks have answered these NCERT questions. These answers will aid students in comprehending and mastering various arithmetic progression questions. Students who attempt to learn without understanding may run into problems while trying to answer questions in their yearly examinations or competitive examinations. NCERT books put a strong emphasis on making topics apparent to students. Students must grasp how to apply the concepts from the NCERT books to comprehend the questions and be able to answer any question about that particular concept. It is crucial to understand how to apply the concepts to particular problems. NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 also includes solutions to significant Class 10 questions.

NCERT Solutions Class 10 Maths Chapter 5 Arithmetic Progression Ex 5.1

CBSE students of Class 10 can easily download solutions of Class 10 Maths Chapter 5 Exercise 5.1. They can download the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 from Extramarks’ website or mobile application in PDF format so that they can study the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 even in offline mode.

Students encounter problems when completing the exercises in NCERT books and generally resolving queries. Students should practise answering the questions with confidence and make an effort to comprehend them. They can download the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 for assistance. Students should remember that even though grades aren’t always taken into account, knowing Class 10 will assist them to pass the competitive examinations. Out of all the subjects, Mathematics has the most significant impact on students’ lives. They must therefore concentrate on mathematics. One of the most complex subjects is Mathematics, which is concept-based. Learning mathematics is beneficial for brain development, and students should practise it regularly to develop quick and sharp thinking. From the time that students were young until they were in Class 10, Mathematics has been a crucial part of their growth. Beginning in Class 1 or Class 2, Mathematics begins teaching students the fundamental concepts of addition, subtraction, multiplication, and division, which will only benefit them when they begin managing their finances. They become good at problem-solving because of their sharp minds, as they will become good at analytical approaches and reasoning. Therefore, NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will also help them to perform better in under-pressure situations.

Students must obtain the aforementioned PDF file from the Extramarks website or mobile application for a better grasp of mathematics. NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 are highly beneficial to students’ development. When someone learns from a specialist in a certain field, they comprehend ideas more clearly. Therefore, the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 should be consulted by students. Undoubtedly, students already know a lot, but a professional’s assessment can help them get a higher score for their responses. Students can learn how experts approach mathematical questions by using the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 and applying that knowledge to their answers. Class 10 may appear to be a lot of pressure to students, but thorough study can overcome any study pressure.The basic understanding of Mathematics in Class 9 and Class 10 will help students build a strong foundation.So, those students who are planning to choose the Science stream after Class 10 must have proper knowledge of Mathematics. There could be a lot of opportunities for those students who will choose Mathematics after Class 10.

Mathematics has a wide range of opportunities, and students who have zeal and enthusiasm can achieve anything with sharp planning and understanding. Before rushing into any stream selection, students should consider what they are interested in. They must weigh the advantages and disadvantages of the choice they will make. The best advice for students is to never panic and to seek support from their parents, instructors, and Extramarks professionals. If students are aware of themselves, this endeavor may not seem as demanding as it first appears. They must have a distinct understanding of and interest in who they are, and then make decisions in line with that understanding. After Class 10, students can choose from the Arts, Commerce, or Science stream. Extramarks is a resource that students can use to learn more about any subject they are interested in. In that process of learning, the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will aid students in grasping syllabus concepts.

The top management and research organisation in the country is NCERT. Students who adhere to the CBSE board curriculum should be aware that, while they can pass the CBSE examinations with decent results by solely studying the NCERT textbooks, doing so can sometimes be challenging. While preparing for their yearly examinations, it would be smart to concentrate solely on NCERT texts. Extramarks has followed the CBSE format. Students will be well-prepared for their examinations with additional NCERT books. Students must complete an exercise after each chapter. To leave no stone unturned in the growth of students, Extramarks has supplied solutions for each exercise in case students are unable to solve the problems. CBSE says that NCERT books are enough to score good enough marks in examinations. The NCERT Solutions for Class 10 Maths, Chapter 5, Exercise 5.1, will assist students in clarifying their concepts for competitive examinations as well.

The National Council of Educational Research and Training (NCERT), an impartial organisation, was founded by the Indian government to assist various public and private schools in India in providing high-quality education. The goal of the NCERT is to establish and uphold a framework for national education while also enabling and supporting a range of cultural activities throughout the nation. The Central Board of Secondary Education (CBSE) and other state boards have already adopted NCERT texts for Classes 1 through 12 into their academic curricula. The NCERT Book is also advised for use when taking several competitive exams, including the Union Public Service Commission (UPSC), CA Foundation Exam, National Eligibility Cum Entrance Test (NEET), and the Joint Entrance Examination (JEE). Since NCERT books are written in a simple, straightforward style. The NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will make students understand the questions of 10th Maths Exercise 5.1.

Although mathematics may appear to be a difficult academic subject, students should be aware that over the centuries, renowned mathematicians from all over the world have contributed to it.The NCERT Solutions for Class 10 Maths, Chapter 5, Exercise 5.1 are written in such a way that students can quickly grasp the concepts.NCERT books are written with the idea of what students’ minds can comprehend at a given age in mind, and are based on that age.The NCERT textbooks’ goal is for students to grow intellectually. The Extramarks online learning platform has assembled NCERT Solutions to support students in their academic endeavours while keeping in mind the structure of NCERT books. Physics, Chemistry, Economics, Engineering, and other areas have all benefited from the use of Mathematics. Mathematics is required to fully comprehend some topics in these areas. From home to an art gallery, mathematics is literary everywhere. Mathematics can be found in all kinds of things, including forms, shapes, sizes, temperatures, degrees, finance, time, and watches. The NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will be available for students’ use online and offline.In some curricula, Mathematics is taught as an “instrumental subject” to support the study of other disciplines, while in others, integrated courses that combine Mathematics and other subjects are also offered.

Access NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progression

All the tools required for competitive exam preparation are available on the Extramarks website and mobile application. Students can use Extramarks to help them get ready for a variety of competitive exams, including JEE Mains, NEET, JEE Advance, CUET, and others. Extramarks provides all the solutions to every chapter and subject. Students can go to the website of Extramarks and access the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 in PDF format for further assistance regarding that chapter.

Students must know that basic Class 10 level Mathematics gets asked in every competitive examination and to qualify for those examinations easily, students must focus on Mathematics in Class 10 only with the help of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1. Students are advised to fully retain each and every chapter of Class 10 to score well in the Class 10 board examination. Class 10 marks are considered important for students as these marks will help themto get into the desired stream they want to choose. Class 10 marks play a vital role in shaping the academic future of a student. Therefore, they must get focused from the very beginning. Those students who want to excel in the Class 10 board examination, should follow the patterns of the NCERT book and get help from NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1. Students are advised that practise is the key to performing well in exams, and those who practise mathematical problems on a daily basis will not face any complexities in exams.Students must be sincere while solving the questions, as understanding the concepts while solving the questions will help them in the long run. This foundational knowledge of Mathematics will help students  qualify for vast competitive examinations like the Joint Entrance Examination (JEE). Students must have a clear vision before rushing into any stream, as this decision will help shape their future. The NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will help students to have a clear concept while taking on such big discussions in their lives.

Students should adhere to the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1since it was designed with the assistance of knowledgeable professionals in mathematics. If students understand the NCERT Solutions they will easily solve them, which will help them decide what career path to take after class 10. When students are unsure of what to do after Class 10, it might be hard for them. Class 10 might be tough at times, so students should become familiar with it right away. Students are recommended to consistently study and maintain focus on their areas of weakness. They must continue to use the Extramarks NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 since Extramarks will always be available to aid them. Students must know that Mathematics after Class 10 will only get more complex, which is why they must get well-prepared to face such challenges. The Maths Class 10 Chapter 5 Exercise 5.1 is essential for all students because it establishes a foundational understanding of the chapter.

Students need to understand that Extramarks is a platform where they can receive support and encouragement from knowledgeable teachers in every particular subject area. For a quick review of the material, the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will be beneficial. NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 can be easily used by students, who can depend on it for all of their questions and concerns. NCERT Solutions for Class 10 Maths Chapter 5 Exercise 5.1 is helping students achieve their goals by utilising knowledgeable academics and extensive research using simple language and techniques.

NCERT Solutions for Class 10 Maths – Exercise 5.1

There are a total of 15 chapters in Class 10, and each chapter is important for the understanding of students. Students must go through each chapter and  answer every question in the chapters. The NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will help out students whenever they  get stuck on any question from the exercise. Extramarks provides solutions for every chapter and exercise of Class 10 and more. Students must have a clear concept while solving any question. They are advised to go through the syllabus of Class 10 Mathematics and then organise their study schedule accordingly. There are a total of 4 questions in exercise 5.1 of Chapter Arithmetic Progression. As question number one has four questions, each of which has four sub-questions.Then question 2 has 5 questions, question 3 has 4 questions, and finally question 4 has 15 questions. The exercise may seem short, but it has many sub-questions that could be challenging for students to solve, and NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will help students solve every question. Students must attempt to solve each question independently after consulting NCERT Solutions for Class 10 Maths Chapter 5 Exercise 5.1.The methods and solutions are the easiest available on the internet. Students can follow the steps of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 to score better in examinations. Students will see a rise in their marks if they follow the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1. Students are advised to take each and every exercise seriously and solve them again and again until they have a clear understanding of them. Students will definitely score well if they follow the routine and give proper time to every subject and topic.

NCERT Solutions for Class 10 Maths Chapter 5 Exercise 5.1

Students can download the free PDF of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1. They will get the PDF of  NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 from Extramarks’ website or mobile application so that they can study the materials even in offline mode. Students must not get distracted while solving the questions in the NCERT Mathematics book and solve those questions with full attention.The NCERT Solutions for Class 10 Maths, Chapter 5, Exercise 5.1, are available for free on the Extramarks website or through the Extramarks app.

Downloading the PDF format of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will be helpful for students while solving the questions. Students at times get baffled while solving questions; hence, they must remember that NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will solve all their queries. Students can download the PDF format of  NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 by clicking on the link below.

An Overview of the Topics Covered under NCERT Solutions for Class 10 Maths Chapter 5 – Arithmetic Progressions (Exercise 5.1)

The beginning of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 Arithmetic Progressions provides a few sequence examples to aid students in recognising the various number patterns. The chapter goes into more detail on the terms, common differences, and other terms used in the arithmetic progression. The students will learn that an arithmetic progression is a sequence of numbers where each term can be found by adding a fixed value to the preceding term, leaving aside the first term. The “common difference” is a set value or number that might be positive, negative, or zero. The students must keep in mind that an arithmetic progression often takes the following form: a, a + d, a + 2d, a + 3d,…, where’d’ is a common difference. This NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 demonstrates the differences between finite and infinite arithmetic progression using pertinent examples. A finite AP has the last term, whereas an infinite AP does not.

There are 4 questions in this exercise that thoroughly cover the topic. The students are expected to identify frequent differences and AP sequences, as well as the first few AP terms for the supplied first term. The following link will take students to the pdf of the NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1.

Importance of Class 10 Maths Chapter 5 Arithmetic Progression

The difference between any two consecutive numbers in an arithmetic progression is always the constant value. A typical difference is a name given to the constant value.

The practical use of arithmetic progression:

To figure out how many spectators a stadium can accommodate.

When we take a taxi, we will be charged an initial cost and then a per mile or kilometre charge.

This chapter will help students score well in their examinations, and understanding this chapter will help them use it in their daily lives as well. Therefore, students must solve each and every question in this chapter to prevent being clueless in the examination. The NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 could be a treasure for students in their time of need. That is why students must practise the problems of Arithmetic Progression.

NCERT Solution Class 10 Maths Chapter 5 – Arithmetic Progressions Exercises

As Arithmetic Progression is one of the most important chapters of Class 10. So, students must solve every exercise of the given chapter and Extramarks has provided every solution to each question of Chapter 5- Arithmetic Progression. There are a total of 4 exercises in the given chapter ,and each exercise has been solved by the experts of Mathematics. The first exercise 5.1 has a total number of 4 questions and the second exercise 5.2 has a total number of 20 questions, the third exercise 5.3 has a total number of 20 questions as well, and lastly, the 5.4 exercise is the optional one but students are advised to solve it too. Exercise 5.4 has a total number of 5 questions. Students are advised to solve each and every question in the chapter so that they will not face any issues while solving questions in the examination hall. Extramarks has solved each exercise; the NCERT Solutions for Class 10 Maths Chapter 5 Exercise 5.1 are available on the website.Then NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.2, NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.3, and NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.4, are available on the website of Extramarks and mobile application as well. Students may follow the steps of NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 to have a better understanding of the exercise and chapter.

Class 10 Maths Weightage Marks

The Central Board of Secondary Education’s (CBSE) Class 10 Mathematics curriculum is now accessible. Students can get the Class 10 Mathematics Syllabus for the academic year 2022–2023 from the Extramarks website. The CBSE Mathematics Class 10 Syllabus 2022–23 lists the unit names, themes, and marks assigned for each unit.

Students should complete the class 10 Mathematics curriculum for the years 2022–2032 at least a month before the CBSE Board 10th examinations in 2023. Students should finish the CBSE Class 10 Mathematics Syllabus 2023 as soon as they can. The theory paper of Mathematics will be 80 marks each. Read this article to download the CBSE class 10 Mathematics syllabus 2023 and know the exam pattern and preparation tips.

Benefits of Ex 5.1 Class 10 Maths Solutions

The concept of arithmetic progressions is covered in Chapter 5 of the Class 10 Mathematics NCERT text, which is a particularly fascinating subject. The questions in this chapter can all be quite demanding. Hence, students would have to think logically while solving each question, which is why this might very well be one of the favourite chapters for most students. Students must properly comprehend the chapter with the aid of the Extramarks NCERT solutions. This way, students will be able to have a clear understanding and enjoy their study time simultaneously. Students must know that Exercise 1.5 is one of the important exercises of the chapter. The NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 will help students solve the questions immediately.

Students can also download NCERT Solutions for other classes by clicking the links given below-

NCERT Solutions Class 11

NCERT Solutions class 10

NCERT Solutions Class 9

NCERT Solutions Class 8

NCERT Solutions Class 7

NCERT Solutions class 6

NCERT Solutions Class 5

NCERT Solutions Class 4

NCERT Solutions Class 3

NCERT Solutions Class 2

NCERT Solutions Class 1

Q.1

Write first four terms of the AP, when the first terma and the common difference d are given as follows:(i) a=10, d=10 (ii) a=−2, d=0(iii) a=4, d=−3 (iv) a=−1, d=12(v) a=−1.25, d=−0.25

Ans.

(i) We have,First term=a=10 and Common difference=d=10Now,Second term=a+d=10+10=20,Third term=a+2d=10+2×10=30,Fourth term=a+3d=10+3×10=40,Therefore, first four terms of the AP are:10, 20, 30, 40(ii) We have,First term=a=−2and Common difference=d=0Now,Second term=a+d=−2+0=−2,Third term=a+2d=−2+2×0=−2,Fourth term=a+3d=−2+3×0=−2,Therefore, first four terms of the AP are:−2, −2, −2, −2(iii) We have,First term=a=4and Common difference=d=−3Now,Second term=a+d=4−3=1,Third term=a+2d=4+2×(−3)=−2,Fourth term=a+3d=4+3×(−3)=−5,Therefore, first four terms of the AP are:4, 1,  −2,  −5(iv) We have,First term=a=−1and Common difference=d=12Now,Second term=a+d=−1+12=−12Third term=a+2d=−1+2×12=0Fourth term=a+3d=−1+3×12=12Therefore, first four terms of the AP are:−1, −12, 0, 12(v)We have,First term=a=−1.25and Common difference=d=−0.25Now,Second term=a+d=−1.25−0.25=−1.50,Third term=a+2d=−1.25+2×(−0.25)=−1.75,Fourth term=a+3d=−1.25+3×(−0.25)=−2,Therefore, first four terms of the AP are:−1.25, −1.50,  −1.75,  −2

Q.2

For the following APs, write the first term and thecommon difference:(i) 3,  1, −1, −3, . . . (ii)−5,  −1, 3, 7, . . .(iii) 13,  53, 93,  133,. . . (iv) 0.6, 1.7, 2.8, 3.9, . . .

Ans.

(i) Following is the given AP. 3,  1, −1, −3, . . . Here, first term=3andcommon difference =difference between a term and                                               its preceding term                                            =1−3=−2(ii) Following is the given AP. −5,  −1,  3,  7, . . . Here, first term=−5andcommon difference =difference between a term and                                               its preceding term                                            =−1−5=−6(iii) Following is the given AP. 13,   53, 93, 139, . . . Here, first term=13andcommon difference =difference between a term and                                               its preceding term                                            =53−13=43(iv) Following is the given AP. 0.6, 1.7, 2.8, 3.9, . . . Here, first term=0.6andcommon difference =difference between a term and                                               its preceding term                                            =1.7−0.6= 1.1

Q.3

Which of the following are APs? If they form an AP,find the common difference d and write three moreterms.(i) 2, 4, 8, 16, . . .(ii) 2, 52, 3, 72, . . .(iii) −1.2, −3.2, −5.2, −7.2, . . .(iv) −10, −6,−2, 2, . . .(v) 3, 3+2,  3+22,  3+32,  . . .(vi) 0.2, 0.22, 0.222, 0.2222,  . . .(vii) 0, −4, −8, −12, . . .(viii) −12, −12, −12, −12, . . .(ix) 1, 3, 9, 27, ...(x) a, 2a, 3a, 4a, ...(xi) a, a2, a3, a4, ...(xii) 2, 8, 18, 32, ...(xiii) 3, 6, 9, 12, ...(xiv) 12, 32, 52, 72, ...(xv) 12, 52, 72, 73, ...

Ans.

(i) 2, 4, 8, 16, . . .Here, 4−2=2≠8−4 Therefore, the given list of numbers is not an AP.(ii) 2, 52, 3, 72, . . .We have, a2−a1=52−2=12 a3−a2=3−52=12 a4−a3=72−3=12i.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=12.The next three terms are: 72+12=4,  4+12=92 and 92+12=5.(iii) −1.2, −3.2, −5.2, −7.2, . . .We have, a2−a1=−3.2−(−1.2)=−3.2+1.2=−2 a3−a2=−5.2−(−3.2)=−5.2+3.2=−2 a4−a3=−7.2−(−5.2)=−7.2+5.2=−2i.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=−2.The next three terms are: −7.2−2=−9.2,  −9.2−2=−11.2 and −11.2−2=−13.2.(iv) −10, −6,−2, 2, . . .We have, a2−a1=−6−(−10)=−6+10=4 a3−a2=−2−(−6)=−2+6=4 a4−a3=2−(−2)=2+2=4i.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=4.The next three terms are: 2+4=6,  6+4=10 and 10+4=14.(v) 3, 3+2,  3+22,  3+32,  . . .We have, a2−a1=3+2−3=2 a3−a2=3+22−(3+2)=2 a4−a3=3+32−(3+22)=2i.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=2.The next three terms are: 3+32+2=3+42,  3+42+2=3+52 and 3+52+2=3+62.(vi) 0.2, 0.22, 0.222, 0.2222,  . . .We have, a2−a1=0.22−0.2=0.02 a3−a2=0.222−0.22=0.002So, a2−a1≠a3−a2Therefore, the given list of numbers is not an AP. (vii) 0, −4, −8, −12, . . .We have, a2−a1=−4−0=−4 a3−a2=−8−(−4)=−8+4=−4 a4−a3=−12−(−8)=−12+8=−4i.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=−4.The next three terms are: −12−4=−16,  −16−4=−20and −20−4=−24.(viii) −12, −12, −12, −12,  . . .Obviously, ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=0.The next three terms are: −12, −12, −12.(ix) 1, 3, 9, 27, ...We have, a2−a1=3−1=2 a3−a2=9−3=6So, a2−a1≠a3−a2Therefore, the given list of numbers is not an AP. (x) a, 2a, 3a, 4a, ...We have, a2−a1=2a−a=a a3−a2=3a−2a=a a4−a3=4a−3a=ai.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=a.The next three terms are: 4a+a=5a,  5a+a=6aand 6a+a=7a.(xi) a, a2, a3, a4, ...Obviously, ak+1−ak is not the same every time.Therefore, the given list of numbers is not an AP.(xii) 2, 8, 18, 32, ...We have, a2−a1=8−2=22−2=2 a3−a2=18−8=32−22=2 a4−a3=32−18=42−32=2i.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=2.The next three terms are: 32+2=42+2=52=50,  50+2=52+2=62=72 and 72+2=62+2=72=98.(xiii) 3, 6, 9, 12, ...We have, a2−a1=6−3=2×3−3=32−1 a3−a2=9−6=3×3−2×3=33−2So, a2−a1≠a3−a2Therefore, the given list of numbers is not an AP. (xiv) 12, 32, 52, 72, ...We have, a2−a1=32−12=9−1=8 a3−a2=52−32=25−9=16So, a2−a1≠a3−a2Therefore, the given list of numbers is not an AP. (xv) 12, 52, 72, 73, ...We have, a2−a1=52−12=25−1=24 a3−a2=72−52=49−25=24          a4−a3=73−72=73−49=24i.e., ak+1−ak is the same every time.Therefore, the given list of numbers is an AP with the commondifference d=24.The next three terms are: 73+24=97,  97+24=121 and 121+24=145.

Q.4 Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:

Ans.

(i) We have a=7,    d=3,    n=8We know that      an=a+(n−1)d⇒an=7+(8−1)3=28(ii) We have a=−18,  n=10, an=0We know that      an=a+(n−1)d⇒0=−18+(10−1)d⇒d=189=2(iii) We have d=−3, n=18, an=−5We know that      an=a+(n−1)d⇒−5=a+(18−1)(−3)⇒a=51−5=46(iv) We have a=−18.9,  d=2.5, an=3.6We know that      an=a+(n−1)d⇒3.6=−18.9+(n−1)(2.5)⇒(n−1)(2.5)=3.6+18.9=22.5⇒n=22.52.5+1=10(v) We have a=3.5,    d=0,    n=105We know that      an=a+(n−1)d⇒an=3.5+(105−1)×0=3.5

Please register to view this section

FAQs (Frequently Asked Questions)

1. Are NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 solved topic-wise according to the NCERT book of Maths?

Yes, NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 has been solved topic-by-topic in accordance with the NCERT Mathematics book. The experts always ensure that NCERT books remain at the center of their study material so that students can easily find it in the book after reading from NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1.

2. How can students access NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1?

Students can get NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 from the Extramarks website and mobile app, and download the PDF format only from there. That is simple to understand and beneficial to students preparing for board examinations and other entrance examinations.

3. Is it helpful to download NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1?

Yes, without a doubt, downloading NCERT Solutions For Class 10 Maths Chapter 5 Exercise 5.1 is very beneficial because they are topic-wise notes and solutions to NCERT questions, so students do not have to worry about anything. They only have to focus on studying minutely and in the end, they will be able to solve all their confusion.