CA Foundation Exam > CA Foundation Questions > [105] The sum of three numbers in a geometric...
Start Learning for Free
[105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336?
Most Upvoted Answer
[105] The sum of three numbers in a geometric progression is 28. When ...
Solution:
Let the three numbers be a, ar and ar^2.
Given, a + ar + ar^2 = 28
Subtracting 7, 2 and 1 from a, ar and ar^2 respectively, we get a - 7, ar - 2 and ar^2 - 1.
We are given that (a - 7), (ar - 2) and (ar^2 - 1) are in arithmetic progression.
Therefore, 2(ar - 2) = (a - 7) + (ar^2 - 1)
Simplifying this, we get ar^2 - 2ar - a + 3 = 0
This is a quadratic equation in r, which can be solved as follows:
ar^2 - 2ar - a + 3 = 0
(ar - 3)(r + 1) = 0
Therefore, r = 3/a or r = -1
Case 1: r = 3/a
In this case, the three numbers are a, 3a and 9a.
Sum of squares of these numbers = a^2 + 9a^2 + 81a^2 = 91a^2
Substituting the value of a + ar + ar^2 = 28, we get:
a + 3a + 9a = 28
Solving this, we get a = 4/3
Therefore, the sum of squares of the original three numbers in this case = 91(4/3)^2 = 121.33
Case 2: r = -1
In this case, the three numbers are a, -a and a.
Sum of squares of these numbers = a^2 + a^2 + a^2 = 3a^2
Substituting the value of a + ar + ar^2 = 28, we get:
a - a + a = 28
Solving this, we get a = 14
Therefore, the sum of squares of the original three numbers in this case = 3(14)^2 = 588
Hence, the correct answer is (c) 400.
Let the three numbers be a, ar and ar^2.
Given, a + ar + ar^2 = 28
Subtracting 7, 2 and 1 from a, ar and ar^2 respectively, we get a - 7, ar - 2 and ar^2 - 1.
We are given that (a - 7), (ar - 2) and (ar^2 - 1) are in arithmetic progression.
Therefore, 2(ar - 2) = (a - 7) + (ar^2 - 1)
Simplifying this, we get ar^2 - 2ar - a + 3 = 0
This is a quadratic equation in r, which can be solved as follows:
ar^2 - 2ar - a + 3 = 0
(ar - 3)(r + 1) = 0
Therefore, r = 3/a or r = -1
Case 1: r = 3/a
In this case, the three numbers are a, 3a and 9a.
Sum of squares of these numbers = a^2 + 9a^2 + 81a^2 = 91a^2
Substituting the value of a + ar + ar^2 = 28, we get:
a + 3a + 9a = 28
Solving this, we get a = 4/3
Therefore, the sum of squares of the original three numbers in this case = 91(4/3)^2 = 121.33
Case 2: r = -1
In this case, the three numbers are a, -a and a.
Sum of squares of these numbers = a^2 + a^2 + a^2 = 3a^2
Substituting the value of a + ar + ar^2 = 28, we get:
a - a + a = 28
Solving this, we get a = 14
Therefore, the sum of squares of the original three numbers in this case = 3(14)^2 = 588
Hence, the correct answer is (c) 400.
Community Answer
[105] The sum of three numbers in a geometric progression is 28. When ...
D 336
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
[105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336?
Question Description
[105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336?.
[105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336?.
Solutions for [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? defined & explained in the simplest way possible. Besides giving the explanation of
[105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336?, a detailed solution for [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? has been provided alongside types of [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? theory, EduRev gives you an
ample number of questions to practice [105] The sum of three numbers in a geometric progression is 28. When 7, 2 and 1 are subtracted from the first, second and the third numbers respectively, then the resulting numbers are in arithmetic progression. What is the sum of squares of the original three numbers? (a) 510 (b) 456 (c) 400 (d) 336? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup