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NCERT exemplar Class 10 Maths solutions chapter 5 provides the understanding for arithmetic progressions. Arithmetic Progressions is a very useful concept and can be used as a tool to generate useful value from a given set of data. The NCERT exemplar Class 10 Maths chapter 5 solutions are prepared by our highly experienced mathematics department and provide all the necessary in-depth concepts required to study NCERT Solutions for Class 10 Maths. These NCERT exemplar Class 10 Maths chapter 5 solutions take into consideration all the basic concepts of arithmetic progression so that students can build a strong foundation. The CBSE Syllabus for Class 10 is incorporated in these NCERT exemplar Class 10 Maths solutions chapter 5.
In an AP, if d = –4, n = 7, an=4, then a is
(A) 6
(B) 7
(C) 20
(D) 28
Answer:
Given
Hence option D is correct
In an AP, if a = 3.5, d = 0, n = 101, then an will be
(A) 0
(B) 3.5
(C) 103.5
(D) 104.5
Answer:
We know that
Hence option B is correct.
Question:3
The list of numbers – 10, – 6, – 2, 2... is
(A) an AP with d = – 16
(B) an AP with d = 4
(C) an AP with d = – 4
(D) not an AP
Answer:
Hence the given sequence is an AP with d = 4
ANS - (B)
Question:4
The 11th term of the AP:
(A) –20
(B) 20
(C) –30
(D) 30
Answer:
Here AP is
Here
Hence option B is correct.
Question:5
The first four terms of an AP, whose first term is –2 and the common difference is –2, are
(A) – 2, 0, 2, 4
(B) – 2, 4, – 8, 16
(C) – 2, – 4, – 6, – 8
(D) – 2, – 4, – 8, –16
Answer:
Given,
Hence the given AP is -2, -4, -6, - 8
Hence option (C) is correct.
Question:6
The 21st term of the AP whose first two terms are –3 and 4 is
(A) 17
(B) 137
(C) 143
(D) –143
Answer:
Given
Hence option B is correct.
Question:7
If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(A) 30
(B) 33
(C) 37
(D) 38
Answer:
We know that
Hence option B is correct.
Question:8
Which term of the AP: 21, 42, 63, 84... is 210?
(A) 9th
(B) 10th
(C) 11th
(D) 12th
Answer:
Here,
Question:9
If the common difference of an AP is 5, then what is ?
(A) 5
(B) 20
(C) 25
(D) 30
Answer:
Given
Option is (C) is correct.
Question:10
What is the common difference of an AP in which ?
(A) 8
(B) – 8
(C) – 4
(D) 4
Answer:
Given,
Hence common difference is 8.
Question:11
Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4th terms is
(A) –1
(B) – 8
(C) 7
(D) –9
Answer:
Hence option (C) is correct
Question:12
If 7 times the 7thterm of an AP is equal to 11 times its 11th term, then its 18thterm will be
(A) 7
(B) 11
(C) 18
(D) 0
Answer:
Hence option D is correct.
Question:13
The 4thterm from the end of the AP: –11, –8, –5, ..., 49 is
(A) 37
(B) 40
(C) 43
(D) 58
Answer:
Hence option B is correct
Question:14
The famous mathematician associated with finding the sum of the first 100 natural numbers is
(A) Pythagoras
(B) Newton
(C) Gauss
(D) Euclid
Answer:
[C]
Famous mathematician gauss find the sum of the first 100 natural numbers.
According to which when he added the first and the last number in the series, the second and the second last number in the series, and so on. He get a sum of 101 and there are 50 pairs exist so the sum of 100 natural numbers is 50×101=5050.
Question:15
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is
(A) 0
(B) 5
(C) 6
(D) 15
Answer:
Hence option A is correct
Question:16
The sum of first 16 terms of the AP: 10, 6, 2... is
(A) –320
(B) 320
(C) –352
(D) –400
Answer:
Hence option A is the correct answer.
Question:18
The sum of first five multiples of 3 is
(A) 45
(B) 55
(C) 65
(D) 75
Answer:
Hence option A is correct.
Answer:
i)
Answer. [True]
Solution.
Here the difference of the successive term is same hence it is an AP.
ii)
Answer. [No]
Solution.
Here the difference successive term is not same. Hence it is not an AP.
iii)
Answer. [No]
Solution.
Here the difference successive term is not the same. Hence it is not an AP.
iv)
Answer. [Yes]
Solution.
Here the difference of the successive term is same. Hence it is an AP.
v)
Answer. [No]
Solution.
Here the difference between the successive terms is not the same. Hence it is not an AP.
vi)
Answer. [No]
Solution.
Here the difference of the successive terms is not the same. Hence it is not an AP.
vii)
Answer. [Yes]
Solution.
Here the difference of the successive term is the same. Hence it is an AP.
Question:3
Answer:
Answer. [True]
Solution. Here the given series is
Question:4
Answer:
Answer. [True]
Solution.
It is given that the first term of an AP is 2 and of other is 7.
it is because when we find the difference between 10th and 21st term it is equal to the a1-b1 which is the difference between first terms.
Question:5
Is 0 a term of the AP: 31, 28, 25, ...? Justify your answer.
Answer:
Answer. [False]
Solution.
Here he given series is 31, 28, 25, …….
Which is not an integer.
Hence 0 is not a term of this AP.
Question:6
Answer:
Answer. [True]
Solution.
Here difference of the successive terms is not same hence it does not form an AP
Therefore given statement is true.
Question:7
Answer:
i)
Answer. [Yes]
Solution.
According to the question:
It is clear that the monthly fee charged from students is = 400 Rs.
Hence series is ; 400, 400, 400, 400 ……
the difference of the successive terms is same so It forms an AP with common difference d = 400 – 400 = 0
ii)
Answer. [Yes]
Solution.
According to the question:
Fees started Rs. 250 and increased by 50 Rs. from I to XII is
It forms an AP with common difference 50.
iii)
Answer. [Yes]
Solution. We know that: Simple interest = (P × R × T)/100
This is definite form an AP with common difference of SI=100 Rs.
iv)
Answer. [No]
Solution.
Let the number of bacteria = x
According to the question:
They double in every second.
Since the difference between the successive terms is not same therefore it does not form an AP.
Question:8
Answer:
i)
Answer. [Yes]
Solution.
Hence, 2n – 3 is the nth term of an AP because the common difference is the same.
ii)
Answer. [No]
Solution.
Here the common difference is not the same
Therefore series is not the nth term of an AP.
iii)
Answer. [No]
Solution.
Here the common difference is not the same
Match the APs given in column A with suitable common differences given in column B.
Column A | Column B |
(A1) 2, – 2, – 6, – 10,... | (B1) |
(A2) a = –18, n = 10, an = 0 | (B2) –5 |
(A3) a = 0, = 6 | (B3) 4 |
(A4) | (B4) –4 |
(B5) 2 | |
(B6) | |
(B7) 5 |
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Answer:
Question:2
Answer:
i)
Here the given series is,
Here the common difference is the same. Hence given series is an AP
Next three terms are
ii)
iii)
iv)
v)
Question:4
Find a, b and c such that the following numbers are in AP: a, 7, b, 23, c.
Answer:
Given AP is a, 7, b, 23, c
We know that if series are in AP then
(We know that the common difference of an A.P is Equal)
Hence a = - 1, b = 15, c = 31
Question:7
The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.
Answer:
Hence the AP is 1, 6, 11....
Question:8
Find the 20th term of the AP whose 7th term is 24 less than the 11thterm, first term being 12.
Answer:
Given a = 12
We know that
Hence
Question:9
If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term.
Answer:
Let first term = a
common difference = d
Given:-
Hence proved
Question:10
Find whether 55 is a term of the AP: 7, 10, 13, ______or not. If yes, find which term it is.
Answer:
Let 55 is the nth term of an AP
Given AP is 7, 10, 13........
Here a = 7, d = 10 - 7
d = 3
By equation (1) is
Here n is a positive integer.
Hence 55 is 17th term of an AP
Question:11
Determine k so that are three consecutive terms of an AP.
Answer:
Here the given AP is
Hence, it is given that these terms are an AP
So the common difference of the A.P
Question:12
Answer:
Let the three parts are (a - d), a, (a + d)
As per the question -
It is given that the product of the two similar parts is 4623
Required numbers are 67, 69, and 71
Question:13
Answer:
Let the three angles are (a - d), a, (a + d) are in AP
According to question the greatest is twice the least
We know that the sum of angles of a triangle is
Required angles
Question:14
Answer:
The given APs are
In AP
Here the number of terms n is equal in both case
According to question
Question:15
Answer:
It is given that the sum of .
Question:16
Find the 12thterm from the end of the AP: -2, -4, -6,..., -100.
Answer:
The given AP : is
AP from end is
Question:19
Find the sum of the two middlemost terms of the AP:
Answer:
Here the given AP is
Let there are n terms in AP
The nth term of AP is
Total terms in this AP is 18 and the middlemost terms and 9thand 10th.
Question:21
Answer:
i)
The given series is
Here
The formula of the sum is :
ii)
iii)
Question:23
Answer:
Here it is given that
Put n =1 then
Put n =2 then
Put n =3 then
Question:30
Find the sum of last ten terms of the AP: 8, 10, 12, __________ , 126.
Answer:
Sum of 10 terms from last-
Question:32
Answer:
Here the given AP is
First term (a) = - 15
Common difference (d) = - 13 - (-15) = - 13 + 15 = 2
Let n terms have sum - 55 then
There are two answers which are 5th when n=5 all terms are negative and 11th terms when n=11 the AP will contain positive numbers and negative terms so the resulting sum is - 55.
Question:34
Answer:
According to the question she puts Rs. 1 on Day 1, 2 on Day 2 and so on.
Total money = Total she put + Spent + left
= 496 + 204 + 100
Total = 800 Rs
Answer:
We know that
Question:2
Answer:
i)
ii)
iii)
The sum of integers from 1 to 500 which are multiples of 2 or 5 = sum of integers which are multiples of 2 + sum of integer which are multiple of 5 - the sum of integer which is multiple of 10
(we subtract the sum of integers multiple of 10 because those integers are multiples of both 2 and 5 )
= 88000 - 12750 = 75250
Question:3
Answer:
According to question
Question:4
Answer:
Total terms = 37, middle term =
Three middle most terms, 18th , 19thand 20th, given
Question:5
Answer:
i)
Numbers between 100 and 200 which is divisible by 9 are 108, 117, 126, ... 198.
Here a = 108, d = 117- 108 = 9
ii)
Numbers between 100 and 200 are 101, 102, 103, .. , 199
Here a = 101, d = 102 - 101 = 1
Numbers between 100 and 200 which is divisible by 9 are 108, 117, 126, ...198
Here b = 108,
the sum of the integers between 100 and 200 that is not divisible by 9
=Sum of all numbers - the sum of numbers which is divisible by 9
Question:7
Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to
Answer:
Here
Hence proved.
Question:9
Answer:1
Total loan = 118000
First installment (a) = 1000
Installment increased = 100
Hence d = 100
= 1000 + 29(100)
= 1000 + 2900
= 3900
Amount of loan paid after 30 installments
= Total loan - 30th installments is total loan
Question:10
Answer:
Let she fixes 13 flags on one side and 13 on other side of the middle flag.
distance covered for fixing first flag and return is 2m + 2m = 4m
distance covered for fixing second flag and return is 4m + 4m = 8m
distance covered for fixing third flag and return is 6m + 6m = 12m
Similarly for thirteen flags is
4m + 8m + 12m + …….
Here, a = 4
d = 8 - 4 = 4
n = 13
Total distance covered = 364 × 2 = 728 m (for both side )
distance, only to carry the flag = 364.
These Class 10 Maths NCERT exemplar chapter 5 solutions provide a detailed knowledge of arithmetic progression. Progression is defined as a sequence of numbers in which numbers progress in some given order. Generally, there are arithmetic progressions, geometric progressions, and harmonic progressions. The quantity and quality of questions covered in the exemplar are sufficient for a student to solve most of the Arithmetic Progressions based practice problems.
If a student diligently practices and understands the Class 10 Maths NCERT exemplar solutions chapter 5 Arithmetic Progressions, solving other books such as A textbook of Mathematics by Monica Kapoor, NCERT Class 10 Maths, RS Aggarwal Class 10 Maths, RD Sharma Class 10 Maths, et cetera won’t be of any issue.
Careers 360 is highly dedicated to provide the students with a strong and sound learning curve and for this reason, NCERT exemplar Class 10 Maths solutions chapter 5 pdf download feature is available to provide a seamless experience while studying NCERT exemplar Class 10 Maths chapter 5.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
Yes, they can have same common difference but they must have different first term then only these two progressions will be considered as different progression
Yes, the summation of AP can be zero but for that exactly one first term or common difference has to be negative and other has to be positive.
Yes, the knowledge of AP given in class 10 is more than sufficient for solving any questions of AP at a higher level. If any student refers NCERT exemplar Class 10 Maths solutions chapter 5, it would be very useful for mathematics at higher levels
This chapter is important for Class 10 board exams as it comprises around 4-5% weightage of the whole paper.
Generally, Arithmetics progression is considered among the important topics for board examinations and accounts for 8-10% marks of the total paper.
Dear aspirant !
Hope you are doing well ! The class 10 Hindi mp board sample paper can be found on the given link below . Set your time and give your best in the sample paper it will lead to great results ,many students are already doing so .
Hope you get it !
Thanking you
Hello aspirant,
The dates of the CBSE Class 10th and Class 12 exams are February 15–March 13, 2024 and February 15–April 2, 2024, respectively. You may obtain the CBSE exam date sheet 2024 PDF from the official CBSE website, cbse.gov.in.
To get the complete datesheet, you can visit our website by clicking on the link given below.
https://school.careers360.com/boards/cbse/cbse-date-sheet
Thank you
Hope this information helps you.
Hello aspirant,
The paper of class 7th is not issued by respective boards so I can not find it on the board's website. You should definitely try to search for it from the website of your school and can also take advise of your seniors for the same.
You don't need to worry. The class 7th paper will be simple and made by your own school teachers.
Thank you
Hope it helps you.
The eligibility age criteria for class 10th CBSE is 14 years of age. Since your son will be 15 years of age in 2024, he will be eligible to give the exam.
That totally depends on what you are aiming for. The replacement of marks of additional subjects and the main subject is not like you will get the marks of IT on your Hindi section. It runs like when you calculate your total percentage you have got, you can replace your lowest marks of the main subjects from the marks of the additional subject since CBSE schools goes for the best five marks for the calculation of final percentage of the students.
However, for the admission procedures in different schools after 10th, it depends on the schools to consider the percentage of main five subjects or the best five subjects to admit the student in their schools.
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Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.
An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.
They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.
Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.
The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.
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