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NCERT Solutions for Exercise 5.1 Class 10 Maths Chapter 5 Arithmetic Progressions are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. This class 10 ex 5.1 the focus is on the general equation of arithmetic progression along with the general equation it includes many problems based on common difference and first term. Class 10 maths ex 5.1 also gives a very small idea about finite and infinite A.P series.
NCERT solutions for 10th class Maths exercise 5.1 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Arithmetic Progressions Class 10 Chapter 5 Exercise: 5.1
Q1 (i) In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (i) The taxi fare after each km when the fare is for the first km and for each additional .
Answer:
It is given that
Fare for = Rs. 15
And after that for each additional
Now,
Fare for = Fare of first km + Additional fare for 1 km
= Rs. 15 + 8 = Rs 23
Fare for = Fare of first km + Fare of additional second km + Fare of additional third km
= Rs. 23 + 8= Rs 31
Fare of n km =
( We multiplied by n - 1 because the first km was fixed and for the rest, we are adding additional fare.
In this, each subsequent term is obtained by adding a fixed number (8) to the previous term.)
Now, we can clearly see that this is an A.P. with the first term (a) = 15 and common difference (d) = 8
Q1 (ii) In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (ii) The amount of air present in a cylinder when a vacuum pump removes of the air remaining in the cylinder at a time.
Answer:
It is given that
vacum pump removes of the air remaining in the cylinder at a time
Let us take initial quantity of air = 1
Now, the quantity of air removed in first step = 1/4
Remaining quantity after 1 st step
Similarly, Quantity removed after 2 nd step = Quantity removed in first step Remaining quantity after 1 st step
Now,
Remaining quantity after 2 nd step would be = Remaining quantity after 1 st step - Quantity removed after 2 nd step
Now, we can clearly see that
After the second step the difference between second and first and first and initial step is not the same, hence
the common difference (d) is not the same after every step
Therefore, it is not an AP
Q1 (iii) In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (iii) The cost of digging a well after every meter of digging, when it costs for the first metre and rises by for each subsequent meter.
Answer:
It is given that
Cost of digging of 1st meter = Rs 150
and
rises by for each subsequent meter
Therefore,
Cost of digging of first 2 meters = cost of digging of first meter + cost of digging additional meter
Cost of digging of first 2 meters = 150 + 50
= Rs 200
Similarly,
Cost of digging of first 3 meters = cost of digging of first 2 meters + cost of digging of additional meter
Cost of digging of first 3 meters = 200 + 50
= Rs 250
We can clearly see that 150, 200,250, ... is in AP with each subsequent term is obtained by adding a fixed number (50) to the previous term.
Therefore, it is an AP with first term (a) = 150 and common difference (d) = 50
Q1 (iv) In which of the following situations, does the list of numbers involved make an arithmetic progression, and why? (iv) The amount of money in the account every year, when is deposited at compound interest at per annum .
Answer:
Amount in the beginning = Rs. 10000
Interest at the end of 1st year at the rate of
is of 10000 =
Therefore, amount at the end of 1st year will be
= 10000 + 800
= 10800
Now,
Interest at the end of 2nd year at rate of
is of 10800 =
Therefore,, amount at the end of 2 nd year
= 10800 + 864 = 11664
Since each subsequent term is not obtained by adding a unique number to the previous term; hence, it is not an AP
Answer:
It is given that
Now,
Therefore, the first four terms of the given series are 10,20,30,40
Q2 (ii) Write first four terms of the AP when the first term a and the common difference d are given as follows:
Answer:
It is given that
Now,
Therefore, the first four terms of the given series are -2,-2,-2,-2
Answer:
It is given that
Now,
Therefore, the first four terms of the given series are 4,1,-2,-5
Answer:
It is given that
Now,
Therefore, the first four terms of the given series are
Answer:
It is given that
Now,
Therefore, the first four terms of the given series are -1.25,-1.50,-1.75,-2
Q3 (i) For the following APs, write the first term and the common difference:
Answer:
Given AP series is
Now, first term of this AP series is 3
Therefore,
First-term of AP series (a) = 3
Now,
And common difference (d) =
Therefore, first term and common difference is 3 and -2 respectively
Q3 (ii) For the following APs, write the first term and the common difference:
Answer:
Given AP series is
Now, the first term of this AP series is -5
Therefore,
First-term of AP series (a) = -5
Now,
And common difference (d) =
Therefore, the first term and the common difference is -5 and 4 respectively
Q3 (iii) For the following APs, write the first term and the common difference:
Answer:
Given AP series is
Now, the first term of this AP series is
Therefore,
The first term of AP series (a) =
Now,
And common difference (d) =
Therefore, the first term and the common difference is and respectively
Q3 (iv) For the following APs, write the first term and the common difference:
Answer:
Given AP series is
Now, the first term of this AP series is 0.6
Therefore,
First-term of AP series (a) = 0.6
Now,
And common difference (d) =
Therefore, the first term and the common difference is 0.6 and 1.1 respectively.
Answer:
Given series is
Now,
the first term to this series is = 2
Now,
We can clearly see that the difference between terms are not equal
Hence, given series is not an AP
Answer:
Given series is
Now,
first term to this series is = 2
Now,
We can clearly see that the difference between terms are equal and equal to
Hence, given series is in AP
Now, the next three terms are
Therefore, next three terms of given series are
Answer:
Given series is
Now,
the first term to this series is = -1.2
Now,
We can clearly see that the difference between terms are equal and equal to -2
Hence, given series is in AP
Now, the next three terms are
Therefore, next three terms of given series are -9.2,-11.2,-13.2
Answer:
Given series is
Now,
the first term to this series is = -10
Now,
We can clearly see that the difference between terms are equal and equal to 4
Hence, given series is in AP
Now, the next three terms are
Therefore, next three terms of given series are 6,10,14
Answer:
Given series is
Now,
the first term to this series is = 3
Now,
We can clearly see that the difference between terms are equal and equal to
Hence, given series is in AP
Now, the next three terms are
Therefore, next three terms of given series are
Answer:
Given series is
Now,
the first term to this series is = 0.2
Now,
We can clearly see that the difference between terms are not equal
Hence, given series is not an AP
Answer:
Given series is
Now,
first term to this series is = 0
Now,
We can clearly see that the difference between terms are equal and equal to -4
Hence, given series is in AP
Now, the next three terms are
Therefore, the next three terms of given series are -16,-20,-24
Q4 (viii) Which of the following are APs? If they form an AP, find the common difference d and write three more terms.
Answer:
Given series is
Now,
the first term to this series is =
Now,
We can clearly see that the difference between terms are equal and equal to 0
Hence, given series is in AP
Now, the next three terms are
Therefore, the next three terms of given series are
Answer:
Given series is
Now,
the first term to this series is = 1
Now,
We can clearly see that the difference between terms are not equal
Hence, given series is not an AP
Answer:
Given series is
Now,
the first term to this series is = a
Now,
We can clearly see that the difference between terms are equal and equal to a
Hence, given series is in AP
Now, the next three terms are
Therefore, next three terms of given series are 5a,6a,7a
Q4 (xi) Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
Answer:
Given series is
Now,
the first term to this series is = a
Now,
We can clearly see that the difference between terms are not equal
Hence, given series is not in AP
Answer:
Given series is
We can rewrite it as
Now,
first term to this series is = a
Now,
We can clearly see that difference between terms are equal and equal to
Hence, given series is in AP
Now, the next three terms are
Therefore, next three terms of given series are
That is the next three terms are
Answer:
Given series is
Now,
the first term to this series is =
Now,
We can clearly see that the difference between terms are not equal
Hence, given series is not in AP
Answer:
Given series is
we can rewrite it as
Now,
the first term to this series is = 1
Now,
We can clearly see that the difference between terms are not equal
Hence, given series is not in AP
Q4 (xv) Which of the following are APs ? If they form an AP, find the common difference d and write three more terms.
Answer:
Given series is
we can rewrite it as
Now,
the first term to this series is = 1
Now,
We can clearly see that the difference between terms are equal and equal to 24
Hence, given series is in AP
Now, the next three terms are
Therefore, the next three terms of given series are 97,121,145
The problems in exercise 5.1 for Class 10 Maths are divided into four categories. Firstly we have a very basic question we have been given scenarios and we have to tell whether it is A.P or not then we have direct questions in which we have been given first term and common difference and we have to find the A.P series NCERT solutions for Class 10 Maths exercise 5.1 also consist of question in which we have to find first term and common difference and also we have question-based on finding whether series is AP or not and if it has to write more terms. All sorts of fundamental problems based on the AP general equation, first term, and common difference are covered in exercise 5.1 Class 10 Maths. Students can quickly go through the Arithmetic Progressions Class 10 Notes to revise all concepts all together.
Exercise 5.1 Class 10 Maths, is based on the general idea about arithmetic progression, which is important for building other concepts of the chapter.
Also see-
Arithmetic progression is a series of numbers in which each term is obtained by adding a constant number to the next term except the first term.
The general equation of the A.P series is a, a+d, a+2d and so on.
A very basic example of A.P series is 1,2,3,4 in which the first term is 1 and the common difference is also 1.
Common differences can be zero, positive and even negative.
Yes, it is considered A.P series as in exercise 5.1 Class 10 Maths it is clearly stated common difference can be zero so it is an AP series with a common difference zero.
The finite A.P series has limited-term while the infinite A.P series has unlimited terms and it never ends.
Before the Class 10 Mathematics chapter 5 exercise 5.1, there are two primary questions that must be answered.
There are 4 questions in Class 10th Maths chapter exercise 5.1. Question 1 consist of four subparts.
Question 2 consists of 5 subparts. Question 3 consists of four subparts. Question 1 consists of 15 subparts
Exam Date:28 April,2024 - 28 April,2024
Exam Date:28 April,2024 - 28 April,2024
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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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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