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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-
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
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
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Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
Yes, you can definitely apply for diploma courses after passing 10th CBSE. In fact, there are many diploma programs designed specifically for students who have completed their 10th grade.
Generally, passing 10th CBSE with a minimum percentage (often 50%) is the basic eligibility for diploma courses. Some institutes might have specific subject requirements depending on the diploma specialization.
There is a wide range of diploma courses available in various fields like engineering (e.g., mechanical, civil, computer science), computer applications, animation, fashion design, hospitality management, and many more.
You can pursue diplomas at various institutions like:
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