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NCERT Solutions for Class 10 Maths exercise 5.4 – A progression is a sequence (or a set) of numbers that follow a specific pattern of repetition. We can define Arithmetic Progression as a set of collective numbers where the difference between any two consecutive terms remains the same throughout the series. This difference between the two terms is called the common difference of the AP.
A brief summary is also provided at the end of this NCERT solutions Class 10 Mathematics chapter 5 exercise 5.4, which will aid students in quickly memorising the full chapter as well as the formulas.
The general form of an AP is , , , …
The other formulas to Arithmetic progression are:
For finding nth term:
{where is the common difference and is the first term}
Sum of first n terms:
{where is the common difference and is the first term}
NCERT book Exercise 5.4 Class 10 Maths an optional exercise with a total of 5 questions that may appear difficult at first and will necessitate some brainstorming.
Along with NCERT syllabus Class 10 Maths chapter 5 exercise 5.4 the following exercises are also present.
Q1 Which term of the AP: is its first negative term? [ Hint : Find for ]
Given AP is
Here
Let suppose nth term of the AP is first negative term
Then,
If nth term is negative then
Therefore, first negative term must be 32nd term
It is given that sum of third and seventh terms of an AP are and their product is
Now,
And
put value from equation (i) in (ii) we will get
Now,
case (i)
Then,
case (ii)
Then,
Q3 A ladder has rungs cm apart. (see Fig. ). The rungs decrease uniformly in length from cm at the bottom to cm at the top. If the top and the bottom rungs are m apart, what is the length of the wood required for the rungs? [ Hint: Number of rungs
It is given that
The total distance between the top and bottom rung
Distance between any two rungs = 25 cm
Total number of rungs =
And it is also given that bottom-most rungs is of 45 cm length and topmost is of 25 cm length.As it is given that the length of rungs decrease uniformly, it will form an AP with
Now, we know that
Now, total length of the wood required for the rungs is equal to
Therefore, the total length of the wood required for the rungs is equal to 385 cm
Q4 The houses of a row are numbered consecutively from to . Show that there is a value of such that the sum of the numbers of the houses preceding the house numbered is equal to the sum of the numbers of the houses following it. Find this value of . [ Hint : ]
It is given that the sum of the numbers of the houses preceding the house numbered is equal to the sum of the numbers of the houses following it
And 1,2,3,.....,49 form an AP with a = 1 and d = 1
Now, we know that
Suppose their exist an n term such that ( n < 49)
Now, according to given conditions
Sum of first n - 1 terms of AP = Sum of terms following the nth term
Sum of first n - 1 term of AP = Sum of whole AP - Sum of first m terms of AP
i.e.
Given House number are not negative so we reject n = -35
Therefore, the sum of no of houses preceding the house no 35 is equal to the sum of no of houses following the house no 35
It is given that
football ground comprises of steps each of which is m long and Each step has a rise of and a tread of
Now,
The volume required to make the first step =
Similarly,
The volume required to make 2nd step =
And
The volume required to make 3rd step =
And so on
We can clearly see that this is an AP with
Now, the total volume of concrete required to build the terrace of 15 such step is
Therefore, the total volume of concrete required to build the terrace of 15 such steps is
NCERT solutions Class 10 Maths chapter 5 exercise 5.4 – This exercise features questions based on realistic real-life scenarios. One question, for example, is based on the ladder notion, and students must compute the length of the wood. Solving this optional exercise 5.4 Class 10 Maths will help us grasp the concept of arithmetic progression deeply. It will also be helpful for us to use the formula to get the sum of the first ‘n’ number of terms or to get a particular term of an arithmetic series. Students should practise many variants of this question because problems like this are frequently asked in board exams.
Also Read| Arithmetic Progressions Class 10 Notes
Class 10 Maths chapter 5 exercise 5.4 is based on practical use of Arithmetic Progression and its Use.
NCERT solutions for Class 10 Maths chapter 5 exercise 5.4 helps in solving and revising all questions which are related to the previous exercises.
If you go through Class 10 Maths chapter 5 exercise 5.4, we can see that the questions are a bit tough, this will help in solving questions that are of higher standards and are difficult.
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Also see-
We can define Arithmetic Progression as a set of collective numbers where the difference between any two consecutive terms remains the same throughout the series. This difference between the two terms is called the common difference of the AP.
The differences between any two consecutive terms are the same which is known as the common difference of the arithmetic progression.
Yes, it the Arithmetic progression is a decreasing one. For example:
15, 12, 9, 6, 3
Common difference =7-4=3
nth term=a+(n-1)d
Where 'a' is the first term and 'd' is the common difference.
First ten natural numbers are 1, 2, 3, .........,10
This is ap with a common difference of 1.
Sum =0.5n(first term+ last term)
=0.5 x 10(1+10)=5 x11=55
Application Date:31 May,2024 - 15 June,2024
Application Date:31 May,2024 - 15 June,2024
Application Date:01 June,2024 - 15 June,2024
Here are some options you can explore to get admission in a good school even though admissions might be closed for many:
Waitlist: Many schools maintain waitlists after their initial application rounds close. If a student who secured a seat decides not to join, the school might reach out to students on the waitlist. So, even if the application deadline has passed, it might be worth inquiring with schools you're interested in if they have a waitlist and if they would consider adding you to it.
Schools with ongoing admissions: Some schools, due to transfers or other reasons, might still have seats available even after the main admission rush. Reach out to the schools directly to see if they have any open seats in 10th grade.
Consider other good schools: There might be other schools in your area that have a good reputation but weren't on your initial list. Research these schools and see if they have any seats available.
Focus on excelling in your current school: If you can't find a new school this year, focus on doing well in your current school. Maintain good grades and get involved in extracurricular activities. This will strengthen your application for next year if you decide to try transferring again.
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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.
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