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The study of number patterns forms a fundamental mathematical aspect which arithmetic progressions enable us to examine. A sequence forms an arithmetic progression when each term differs from its predecessor by a constant amount. When we perform this exercise, we gain insight into how numbered sequences emerge along with methods to calculate absent data points. Through pattern recognition, we learn to generate their own number sequences that establish a connection between mathematical concepts and practical arrangements, together with planning procedures.
In this portion of the NCERT Solutions, your Class 10 Maths students learn to detect arithmetic progressions and determine their common difference and recognise AP structural patterns. The patterns and recognition ability among students improve through their practice of the NCERT Books Exercise 5.1, which will benefit them when solving advanced mathematical problems in higher education. These educational tools enhance analytical thinking skills before students advance to study the topic of the nth term, along with the sum of n terms in an AP.
Answer:
It is given that
Fare for
And after that
Now,
Fare for
= Rs. 15 + 8 = Rs 23
Fare for
= 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
Answer:
It is given that
Vacum pump removes
Let us take an initial quantity of air = 1
Now, the quantity of air removed in the first step = 1/4
Remaining quantity after 1st step
Similarly, Quantity removed after 2nd step = Quantity removed in first step
Now,
Remaining quantity after 2nd step would be = Remaining quantity after 1st step - Quantity removed after 2nd step
Now, we can clearly see that
After the second step, the difference between the 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.
Answer:
It is given that
Cost of digging of 1st meter = Rs 150
And
Rises by
Therefore,
Cost of digging of first 2 meters = cost of digging of first meter + cost of digging the 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 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
Answer:
Amount in the beginning = Rs. 10000
Interest at the end of 1st year at the rate of
is
Therefore, the amount at the end of 1st year will be
= 10000 + 800
= 10800
Now,
Interest at the end of 2nd year at rate of
is
Therefore, the amount at the end of 2nd 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, the first term of this AP series is 3
Therefore,
First term of AP series (a) = 3
Now,
And common difference (d) =
Therefore, the first term and the common difference are 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 are -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
Q3 (iv) For the following APs, write the first term and the common difference:
Answer:
Given the 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 are 0.6 and 1.1, respectively.
Answer:
Given series is
Now,
The first term of this series is = 2
Now,
We can see that the difference between the terms is not equal
Hence, the given series is not an AP.
Answer:
Given series is
Now,
The first term of this series is = 2
Now,
We can clearly see that the difference between terms are equal and equal to
Hence, the given series is in AP.
Now, the next three terms are
Therefore, the next three terms of the given series are
Answer:
Given series is
Now,
The first term of this series is = -1.2
Now,
We can clearly see that the difference between terms are equal and equal to -2
Hence, the given series is in AP.
Now, the next three terms are
Therefore, the next three terms of the given series are -9.2, -11.2, -13.2
Answer:
Given series is
Now,
The first term of this series is = -10
Now,
We can clearly see that the difference between the terms are equal and equal to 4
Hence, the given series is in AP.
Now, the next three terms are
Therefore, the next three terms of the given series are 6,10,14
Answer:
Given series is
Now,
The first term of 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, the 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 the terms is not equal.
Hence, the given series is not an AP
Answer:
Given series is
Now,
the 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 the 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
Also Read-
1. Definition of Arithmetic Progression (AP): Knowledge of Arithmetic Progression (AP) includes its definition and skills for recognising series patterns following this sequence.
2. Common Difference: Calculating the constant difference between consecutive terms in an AP.
3. Identifying APs: Determining whether a given sequence is an AP by analysing the differences between terms.
4. Real-life Applications: Identification and creation of APs occur through recognising such patterns in actual world situations.
5. Extending Sequences: The common difference enables students to find more terms within an arithmetic progression.
Also see-
Students must check the NCERT solutions for class 10 of Mathematics and Science Subjects.
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Students must check the NCERT Exemplar solutions for class 10 of Mathematics and Science Subjects.
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
Admit Card Date:17 April,2025 - 17 May,2025
Exam Date:01 May,2025 - 08 May,2025
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
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.
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