Open App

Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > RD Sharma Solutions: Arithmetic Progressions (Exercise 5B)

Arithmetic Progressions (Exercise 5B) RD Sharma Solutions | Mathematics (Maths) Class 10 PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


1. Determine k so that (3k -2), (4k 6) and (k +2) are three consecutive terms of an AP.
3 2 , 4 6 k k 2 k
Sol:
It is given that and are three consecutive terms of an AP.
4 3 4 k 6
4 6 3 2 4 6
4 3 8
3 8 4
4 12
3
k k k
k k k
k
k k
k
k
6 2 2
2 k
k
Hence, the value of k is 3. 
2.
1 5 2 , 4 x x 2 x
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
Sol:
It is given that and are in AP.
4 5 2 4 x 1
4 1 5 2 2 4 1
3 3
3 3 3
2 x 6
3
x x x
x x x x
x 3 x
x x
x
1 2
Hence, the value of x is 3. 
Page 2


1. Determine k so that (3k -2), (4k 6) and (k +2) are three consecutive terms of an AP.
3 2 , 4 6 k k 2 k
Sol:
It is given that and are three consecutive terms of an AP.
4 3 4 k 6
4 6 3 2 4 6
4 3 8
3 8 4
4 12
3
k k k
k k k
k
k k
k
k
6 2 2
2 k
k
Hence, the value of k is 3. 
2.
1 5 2 , 4 x x 2 x
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
Sol:
It is given that and are in AP.
4 5 2 4 x 1
4 1 5 2 2 4 1
3 3
3 3 3
2 x 6
3
x x x
x x x x
x 3 x
x x
x
1 2
Hence, the value of x is 3. 
 
3. If (3y 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value 
of y.
Sol:
It is given that 3 1 , 3 5 y y and 5 1 y are three consecutive terms of an AP.
3 5 3 1 5 1 3 5
3 5 3 1 5 1 3 5
6 2 4
2 6 4 10
5
y y y y
y y y y
y
y
y
Hence, the value of y is 5.
4. Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
Sol:
Since 2 ,2 x x and 2 3 x are in AP, we have
2 2 2 3 2
2 3
5
5
x x x x
x
x
x
5. Show that 
2
2 2
, a b a b and 
2 2
a b are in AP. 
Sol:
The given numbers are 
2
2 2
, a b a b and 
2
. a b
Now,
2
2 2 2 2 2 2 2 2 2 2
2
2 2 2 2 2 2
2 2 2
2 2
a b a b a b a a b b a b a a b b a b
a b a b a a b b a b a b
So, 
2 2
2 2 2 2
2 a b a b a b a b a b (Constant)
Since each term differs from its preceding term by a constant, therefore, the given numbers 
are in AP.
6. Find the three numbers in AP whose sum is 15 and product is 80.
Sol:
Let the required numbers be , a d a and . a d
Then 15 a d a a d
Page 3


1. Determine k so that (3k -2), (4k 6) and (k +2) are three consecutive terms of an AP.
3 2 , 4 6 k k 2 k
Sol:
It is given that and are three consecutive terms of an AP.
4 3 4 k 6
4 6 3 2 4 6
4 3 8
3 8 4
4 12
3
k k k
k k k
k
k k
k
k
6 2 2
2 k
k
Hence, the value of k is 3. 
2.
1 5 2 , 4 x x 2 x
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
Sol:
It is given that and are in AP.
4 5 2 4 x 1
4 1 5 2 2 4 1
3 3
3 3 3
2 x 6
3
x x x
x x x x
x 3 x
x x
x
1 2
Hence, the value of x is 3. 
 
3. If (3y 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value 
of y.
Sol:
It is given that 3 1 , 3 5 y y and 5 1 y are three consecutive terms of an AP.
3 5 3 1 5 1 3 5
3 5 3 1 5 1 3 5
6 2 4
2 6 4 10
5
y y y y
y y y y
y
y
y
Hence, the value of y is 5.
4. Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
Sol:
Since 2 ,2 x x and 2 3 x are in AP, we have
2 2 2 3 2
2 3
5
5
x x x x
x
x
x
5. Show that 
2
2 2
, a b a b and 
2 2
a b are in AP. 
Sol:
The given numbers are 
2
2 2
, a b a b and 
2
. a b
Now,
2
2 2 2 2 2 2 2 2 2 2
2
2 2 2 2 2 2
2 2 2
2 2
a b a b a b a a b b a b a a b b a b
a b a b a a b b a b a b
So, 
2 2
2 2 2 2
2 a b a b a b a b a b (Constant)
Since each term differs from its preceding term by a constant, therefore, the given numbers 
are in AP.
6. Find the three numbers in AP whose sum is 15 and product is 80.
Sol:
Let the required numbers be , a d a and . a d
Then 15 a d a a d
 
3 15
5
a
a
Also, . . 80 a d a a d
2 2
2
2
80
5 25 80
25 16 9
3
a a d
d
d
d
Thus, 5 a and 3 d
Hence, the required numbers are 2,5 8 8,5 2 . a n d o r a n d
7. The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Sol:
Let the required numbers be , a d a and . a d
Then 3 a d a a d
3 3
1
a
a
Also, . . 35 a d a a d
2 2
2
2
35
1. 1 35
36
6
a a d
d
d
d
Thus, 1 a and 6 d
Hence, the required numbers are 5,1 7 7,1 5 . a n d o r a n d
8. Divide 24 in three parts such that they are in AP and their product is 440.
Sol:
Let the required parts of 24 be , a d a and a d such that they are in AP.
Then 24 a d a a d
3 24
8
a
a
Also, . . 440 a d a a d
2 2
2
440
8 64 440
a a d
d
Page 4


1. Determine k so that (3k -2), (4k 6) and (k +2) are three consecutive terms of an AP.
3 2 , 4 6 k k 2 k
Sol:
It is given that and are three consecutive terms of an AP.
4 3 4 k 6
4 6 3 2 4 6
4 3 8
3 8 4
4 12
3
k k k
k k k
k
k k
k
k
6 2 2
2 k
k
Hence, the value of k is 3. 
2.
1 5 2 , 4 x x 2 x
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
Sol:
It is given that and are in AP.
4 5 2 4 x 1
4 1 5 2 2 4 1
3 3
3 3 3
2 x 6
3
x x x
x x x x
x 3 x
x x
x
1 2
Hence, the value of x is 3. 
 
3. If (3y 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value 
of y.
Sol:
It is given that 3 1 , 3 5 y y and 5 1 y are three consecutive terms of an AP.
3 5 3 1 5 1 3 5
3 5 3 1 5 1 3 5
6 2 4
2 6 4 10
5
y y y y
y y y y
y
y
y
Hence, the value of y is 5.
4. Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
Sol:
Since 2 ,2 x x and 2 3 x are in AP, we have
2 2 2 3 2
2 3
5
5
x x x x
x
x
x
5. Show that 
2
2 2
, a b a b and 
2 2
a b are in AP. 
Sol:
The given numbers are 
2
2 2
, a b a b and 
2
. a b
Now,
2
2 2 2 2 2 2 2 2 2 2
2
2 2 2 2 2 2
2 2 2
2 2
a b a b a b a a b b a b a a b b a b
a b a b a a b b a b a b
So, 
2 2
2 2 2 2
2 a b a b a b a b a b (Constant)
Since each term differs from its preceding term by a constant, therefore, the given numbers 
are in AP.
6. Find the three numbers in AP whose sum is 15 and product is 80.
Sol:
Let the required numbers be , a d a and . a d
Then 15 a d a a d
 
3 15
5
a
a
Also, . . 80 a d a a d
2 2
2
2
80
5 25 80
25 16 9
3
a a d
d
d
d
Thus, 5 a and 3 d
Hence, the required numbers are 2,5 8 8,5 2 . a n d o r a n d
7. The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Sol:
Let the required numbers be , a d a and . a d
Then 3 a d a a d
3 3
1
a
a
Also, . . 35 a d a a d
2 2
2
2
35
1. 1 35
36
6
a a d
d
d
d
Thus, 1 a and 6 d
Hence, the required numbers are 5,1 7 7,1 5 . a n d o r a n d
8. Divide 24 in three parts such that they are in AP and their product is 440.
Sol:
Let the required parts of 24 be , a d a and a d such that they are in AP.
Then 24 a d a a d
3 24
8
a
a
Also, . . 440 a d a a d
2 2
2
440
8 64 440
a a d
d
 
2
64 55 9
3
d
d
Thus, 8 a and 3 d
Hence, the required parts of 24 are 5,8,11 11,8,5 . o r
9. The sum of three consecutive terms of an AP is 21 and the sum of the squares of these 
terms is 165. Find these terms
Sol:
Let the required terms be , a d a and . a d
Then 21 a d a a d
3 21
7
a
a
Also,
2 2
2
165 a d a a d
2 2
2
2
2
3 2 165
3 49 2 165
2 165 147 18
9
3
a d
d
d
d
d
Thus, 7 a and 3 d
Hence, the required terms are 4,7,10 10,7,4 . o r
10. The angles of quadrilateral are in whose AP common difference is 10 . Find the angles.
Sol:
Let the required angles be 15 , 5 , 5 15 , a a a a n d a as the common 
difference is 10 (given).
Then 15 5 5 15 360 a a a a
4 360
90
a
a
Hence, the required angles of a quadrilateral are
90 15 , 90 5 , 90 5 90 15 ; 75 ,85 ,95 105 . a n d o r a n d
11. Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.
Sol:
(4, 6, 8, 10) or (10, 8, 6, 4)
Page 5


1. Determine k so that (3k -2), (4k 6) and (k +2) are three consecutive terms of an AP.
3 2 , 4 6 k k 2 k
Sol:
It is given that and are three consecutive terms of an AP.
4 3 4 k 6
4 6 3 2 4 6
4 3 8
3 8 4
4 12
3
k k k
k k k
k
k k
k
k
6 2 2
2 k
k
Hence, the value of k is 3. 
2.
1 5 2 , 4 x x 2 x
Find the value of x for which the numbers (5x + 2), (4x - 1) and (x + 2) are in AP.
Sol:
It is given that and are in AP.
4 5 2 4 x 1
4 1 5 2 2 4 1
3 3
3 3 3
2 x 6
3
x x x
x x x x
x 3 x
x x
x
1 2
Hence, the value of x is 3. 
 
3. If (3y 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value 
of y.
Sol:
It is given that 3 1 , 3 5 y y and 5 1 y are three consecutive terms of an AP.
3 5 3 1 5 1 3 5
3 5 3 1 5 1 3 5
6 2 4
2 6 4 10
5
y y y y
y y y y
y
y
y
Hence, the value of y is 5.
4. Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
Sol:
Since 2 ,2 x x and 2 3 x are in AP, we have
2 2 2 3 2
2 3
5
5
x x x x
x
x
x
5. Show that 
2
2 2
, a b a b and 
2 2
a b are in AP. 
Sol:
The given numbers are 
2
2 2
, a b a b and 
2
. a b
Now,
2
2 2 2 2 2 2 2 2 2 2
2
2 2 2 2 2 2
2 2 2
2 2
a b a b a b a a b b a b a a b b a b
a b a b a a b b a b a b
So, 
2 2
2 2 2 2
2 a b a b a b a b a b (Constant)
Since each term differs from its preceding term by a constant, therefore, the given numbers 
are in AP.
6. Find the three numbers in AP whose sum is 15 and product is 80.
Sol:
Let the required numbers be , a d a and . a d
Then 15 a d a a d
 
3 15
5
a
a
Also, . . 80 a d a a d
2 2
2
2
80
5 25 80
25 16 9
3
a a d
d
d
d
Thus, 5 a and 3 d
Hence, the required numbers are 2,5 8 8,5 2 . a n d o r a n d
7. The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Sol:
Let the required numbers be , a d a and . a d
Then 3 a d a a d
3 3
1
a
a
Also, . . 35 a d a a d
2 2
2
2
35
1. 1 35
36
6
a a d
d
d
d
Thus, 1 a and 6 d
Hence, the required numbers are 5,1 7 7,1 5 . a n d o r a n d
8. Divide 24 in three parts such that they are in AP and their product is 440.
Sol:
Let the required parts of 24 be , a d a and a d such that they are in AP.
Then 24 a d a a d
3 24
8
a
a
Also, . . 440 a d a a d
2 2
2
440
8 64 440
a a d
d
 
2
64 55 9
3
d
d
Thus, 8 a and 3 d
Hence, the required parts of 24 are 5,8,11 11,8,5 . o r
9. The sum of three consecutive terms of an AP is 21 and the sum of the squares of these 
terms is 165. Find these terms
Sol:
Let the required terms be , a d a and . a d
Then 21 a d a a d
3 21
7
a
a
Also,
2 2
2
165 a d a a d
2 2
2
2
2
3 2 165
3 49 2 165
2 165 147 18
9
3
a d
d
d
d
d
Thus, 7 a and 3 d
Hence, the required terms are 4,7,10 10,7,4 . o r
10. The angles of quadrilateral are in whose AP common difference is 10 . Find the angles.
Sol:
Let the required angles be 15 , 5 , 5 15 , a a a a n d a as the common 
difference is 10 (given).
Then 15 5 5 15 360 a a a a
4 360
90
a
a
Hence, the required angles of a quadrilateral are
90 15 , 90 5 , 90 5 90 15 ; 75 ,85 ,95 105 . a n d o r a n d
11. Find four numbers in AP whose sum is 8 and the sum of whose squares is 216.
Sol:
(4, 6, 8, 10) or (10, 8, 6, 4)
 
12. Divide 32 into four parts which are the four terms of an AP such that the product of the first 
and fourth terms is to product of the second and the third terms as 7:15.
Sol:
Let the four parts in AP be 3 , , 3 . a d a d a d a n d a d Then,
3 3 32
4 32
8 ......... 1
a d a d a d a d
a
a
Also,
2
2
2 2
2 2
2
2
2
3 3 : 7 :15
8 3 8 3
7
(1)
8 8 15
64 9 7
64 15
15 64 9 7 64
960 135 448 7
135 7 960 448
128 512
4
2
a d a d a d a d
d d
F rom
d d
d
d
d d
d d
d d
d
d
d
When 8 a and 2, d
3 8 3 2 8 6 2
8 2 6
8 2 10
3 8 3 2 8 6 14
a d
a d
a d
a d
When 8 a and 2, d
3 8 3 2 8 6 14
8 2 8 2 10
8 2 6
3 8 3 2 8 6 2
a d
a d
a d
a d
Hence, the four parts are 2, 6, 10 and 14.
13. The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 
4 times the third term by 12. Find the AP.
Sol:
Let the first three terms of the AP be , . a d a a n d a d Then,

	Mathematics (Maths) Class 10 123 videos\|457 docs\|77 tests

Mathematics (Maths) Class 10

123 videos|457 docs|77 tests

Join Course for Free

Top Courses for Class 10

View all

Related Exams

Class 10

About this Document

	4.64/5 Rating
	Nov 23, 2024 Last updated

Document Description: RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The notes and questions for RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) have been prepared according to the Class 10 exam syllabus. Information about RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) covers topics like and RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) Example, for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Arithmetic Progressions (Exercise 5B).

Introduction of RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) in English is available as part of our Mathematics (Maths) Class 10 for Class 10 & RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) in Hindi for Mathematics (Maths) Class 10 course. Download more important topics related with notes, lectures and mock test series for Class 10 Exam by signing up for free. Class 10: Arithmetic Progressions (Exercise 5B) RD Sharma Solutions | Mathematics (Maths) Class 10

Description

Full syllabus notes, lecture & questions for Arithmetic Progressions (Exercise 5B) RD Sharma Solutions | Mathematics (Maths) Class 10 - Class 10 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 10 | Best notes, free PDF download

Information about RD Sharma Solutions: Arithmetic Progressions (Exercise 5B)

In this doc you can find the meaning of RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) defined & explained in the simplest way possible. Besides explaining types of RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) tests, examples and also practice Class 10 tests

	Mathematics (Maths) Class 10 123 videos\|457 docs\|77 tests

Mathematics (Maths) Class 10

123 videos|457 docs|77 tests

Join Course for Free

Download as PDF

Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

Semester Notes

Exam

Sample Paper

pdf

Objective type Questions

MCQs

video lectures

past year papers

study material

Important questions

Arithmetic Progressions (Exercise 5B) RD Sharma Solutions | Mathematics (Maths) Class 10

ppt

shortcuts and tricks

Extra Questions

Previous Year Questions with Solutions

practice quizzes

Free

Arithmetic Progressions (Exercise 5B) RD Sharma Solutions | Mathematics (Maths) Class 10

mock tests for examination

Viva Questions

Arithmetic Progressions (Exercise 5B) RD Sharma Solutions | Mathematics (Maths) Class 10

Summary

;

Additional Information about RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) for Class 10 Preparation

RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) Free PDF Download

The RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) is an invaluable resource that delves deep into the core of the Class 10 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) now and kickstart your journey towards success in the Class 10 exam.

Importance of RD Sharma Solutions: Arithmetic Progressions (Exercise 5B)

The importance of RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) cannot be overstated, especially for Class 10 aspirants. This document holds the key to success in the Class 10 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) Notes

RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Solutions: Arithmetic Progressions (Exercise 5B). It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) Notes on EduRev are your ultimate resource for success.

RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) Class 10 Questions

The "RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) on the App

Students of Class 10 can study RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Solutions: Arithmetic Progressions (Exercise 5B), students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Solutions: Arithmetic Progressions (Exercise 5B) is prepared as per the latest Class 10 syllabus.

Education Revolution