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NCERT Solutions for Exercise 5.2 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 202324. This class 10 ex 5.2 the consists of 20 questions solved using the formula of the sum of n terms of the Arithmetic Progression. It also has some word problems too to enhance the understanding of this concept.
NCERT solutions for Exercise 5.2 Class 10 Maths Chapter 5 Arithmetic Progressions focus on the Arithmetic Progression’s basic notion, i.e., how an Arithmetic Progression is formed? Also, it stresses to clear the understanding of the nth term of the Arithmetic Progression. 10th class Maths exercise 5.2 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 Excercise: 5.2
a  d  n 
 
(i) (ii) (iii) (iv) (v)  7
 3
0  8 10 18
105 
0

(i)
It is given that
Now, we know that
Therefore,
(ii) It is given that
Now, we know that
(iii) It is given that
Now, we know that
Therefore,
(iv) It is given that
Now, we know that
Therefore,
(v) It is given that
Now, we know that
Therefore,
Q2 (i) Choose the correct choice in the following and justify: th term of the AP: is
(A) (B) (C) (D)
Given series is
Here,
and
Now, we know that
It is given that
Therefore,
Therefore, th term of the AP: is 77
Hence, Correct answer is (C)
Q2 (ii) Choose the correct choice in the following and justify : 11th term of the AP: is
(A) (B) (C) (D)
Given series is
Here,
and
Now, we know that
It is given that
Therefore,
Therefore, 11th term of the AP: is 22
Hence, the Correct answer is (B)
Q3 (i) In the following APs, find the missing terms in the boxes :
Given AP series is
Here,
Now, we know that
Now,
Therefore, the missing term is 14
Q3 (ii) In the following APs, find the missing terms in the boxes:
Given AP series is
Here,
Now,
Now, we know that
Now,
And
Therefore, missing terms are 18 and 8
AP series is 18,13,8,3
Q3 (iii) In the following APs, find the missing terms in the boxes :
Given AP series is
Here,
Now, we know that
Now,
And
Therefore, missing terms are and 8
AP series is
Q3 (iv) In the following APs, find the missing terms in the boxes :
Answer:
Given AP series is
Here,
Now, we know that
Now,
And
And
And
Therefore, missing terms are 2,0,2,4
AP series is 4,2,0,2,4,6
Q3 (v) In the following APs, find the missing terms in the boxes :
Given AP series is
Here,
Now,
Now, we know that
Now,
And
And
And
Therefore, missing terms are 53,23,8,7
AP series is 53,38,23,8,7,22
Q4 Which term of the AP : is ?
Answer:
Given AP is
Let suppose that nth term of AP is 78
Here,
And
Now, we know that that
Therefore, value of 16th term of given AP is 78
Q5 (i) Find the number of terms in each of the following APs :
Given AP series is
Let's suppose there are n terms in given AP
Then,
And
Now, we know that
Therefore, there are 34 terms in given AP
Q5 (ii) Find the number of terms in each of the following APs :
Given AP series is
suppose there are n terms in given AP
Then,
And
Now, we know that
Therefore, there are 27 terms in given AP
Q6 Check whether is a term of the AP :
Given AP series is
Here,
And
Now,
suppose 150 is nth term of the given AP
Now, we know that
Value of n is not an integer
Therefore, 150 is not a term of AP
Q7 Find the st term of an AP whose th term is and the th term is .
It is given that
th term of an AP is and the th term is
Now,
And
On solving equation (i) and (ii) we will get
Now,
Therefore, 31st terms of given AP is 178
Q8 An AP consists of terms of which rd term is and the last term is . Find the th term.
Answer:
It is given that
AP consists of terms of which rd term is and the last term is
Now,
And
On solving equation (i) and (ii) we will get
Now,
Therefore, 29th term of given AP is 64
Q9 If the rd and the th terms of an AP are and respectively, which term of this AP is zero?
Answer:
It is given that
rd and the th terms of an AP are and respectively
Now,
And
On solving equation (i) and (ii) we will get
Now,
Let nth term of given AP is 0
Then,
Therefore, 5th term of given AP is 0
Q10 The th term of an AP exceeds its th term by . Find the common difference.
Answer:
It is given that
th term of an AP exceeds its th term by
i.e.
Therefore, the common difference of AP is 1
Q11 Which term of the AP : will be more than its th term?
Answer:
Given AP is
Here,
And
Now, let's suppose nth term of given AP is more than its th term
Then,
Therefore, 65th term of given AP is more than its th term
It is given that
Two APs have the same common difference and difference between their th terms is
i.e.
Let common difference of both the AP's is d
Now, difference between 1000th term is
Therefore, difference between 1000th term is 100
Q 13 How many threedigit numbers are divisible by ?
Answer:
We know that the first three digit number divisible by 7 is 105 and last threedigit number divisible by 7 is 994
Therefore,
Let there are n three digit numbers divisible by 7
Now, we know that
Therefore, there are 128 threedigit numbers divisible by 7
Q14 How many multiples of lie between and ?
Answer:
We know that the first number divisible by 4 between 10 to 250 is 12 and last number divisible by 4 is 248
Therefore,
Let there are n numbers divisible by 4
Now, we know that
Therefore, there are 60 numbers between 10 to 250 that are divisible by 4
Q15 For what value of , are the th terms of two APs: and equal?
Given two AP's are
and
Let first term and the common difference of two AP's are a , a' and d , d'
And
Now,
Let nth term of both the AP's are equal
Therefore, the 13th term of both the AP's are equal
Q16 Determine the AP whose third term is and the th term exceeds the th term by .
Answer:
It is given that
3rd term of AP is and the th term exceeds the th term by
i.e.
And
Put the value of d in equation (i) we will get
Now, AP with first term = 4 and common difference = 6 is
4,10,16,22,.....
Q17 Find the th term from the last term of the AP : .
Given AP is
Here,
And
Let suppose there are n terms in the AP
Now, we know that
So, there are 51 terms in the given AP and 20th term from the last will be 32th term from the starting
Therefore,
Therefore, 20th term from the of given AP is 158
It is given that
sum of the < img alt="\small 4" class="frfic frdii" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Csmall%204"> th and th terms of an AP is and the sum of the th and th terms is
i.e.
And
On solving equation (i) and (ii) we will get
Therefore,first three of AP with a = 13 and d = 5 is
13,8,3
It is given that
Subba Rao started work at an annual salary of Rs 5000 and received an increment of Rs 200 each year
Therefore,
Let's suppose after n years his salary will be Rs 7000
Now, we know that
Therefore, after 11 years his salary will be Rs 7000
after 11 years, starting from 1995, his salary will reach to 7000, so we have to add 10 in 1995, because these numbers are in years
Thus , 1995+10 = 2005
It is given that
Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by Rs
Therefore,
after th week, her weekly savings become Rs
Now, we know that
Therefore, after 10 weeks her saving will become Rs 20.75
It's about the nth term of the Arithmetic Progression and deals with the number of terms and rank of the particular term in the Arithmetic Progression. In addition to this, it has word problems that give indepth knowledge of the topic. Exercise 5.2 Class 10 Maths  Arithmetic Progression is the progression in which the difference between two consecutive terms is constant. Using this very concept nth term, a number of terms and rank of a particular term of the progression could be determined. The NCERT solutions for Class 10 Maths exercise 5.2 mainly focuses on the nth term, the validity of the term, and the number of terms in the Arithmetic Progression, and twenty questions are given in exercise 5.2 Class 10 Maths. Students can quickly go through the Arithmetic Progressions Class 10 Notes to revise all concepts all together.
Also see
In Arithmetic Progression, any two consecutive terms differ by a constant numerical value.
It could be calculated easily by using the prop[erty that any two consecutive terms differ by a constant numerical value. To calculate it, just add the difference (n1) times to the first term of the Arithmetic Progression.
For this, just find the rank of that term in that Arithmetic Progression, and if the position comes out to be in fraction, then that term doesn’t belong to that Arithmetic Progression; otherwise, it is.
Yes, it could be done efficiently by using the nth term formula. There would be two unknowns, namely the first term and the common difference, and we would have two equations with us; solving them, we would get those. And once the first term and common difference are calculated then, Arithmetic Progression could be determined.
For this, just do two things i.e.
Take the last term to be the first term.
Reverse the sign of the common difference(if it was +2, do it 2 and vice versa)
Yes, It could be in a fraction. Only the number of terms in the Arithmetic Progression can't be in a fraction.
It's just the generalized way to represent any term of the Arithmetic Progression. Based on the requirement, it could define the first term, last term, etc.
To find the Common Difference of the Arithmetic Progression, just differentiate (n1)th term from the nth term.
According to this exercise, the nth term is any term of the Arithmetic Progression that could be calculated by adding Common Difference (n1) times to the first term of the Arithmetic Progression. This very concept is required to frame the whole Arithmetic Progression.
The questions are based on the concept that the two consecutive terms of the Arithmetic Progression always differ by a constant numerical value. Based on this concept, there are word problems too available in this exercise.
Hello
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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.
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