JEE Exam > JEE Questions > The product of three consecutive terms of a G...
Start Learning for Free
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. is
- a)36
- b)24
- c)32
- d)48
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The product of three consecutive terms of a G.P. is 512. If 4 is added...
Community Answer
The product of three consecutive terms of a G.P. is 512. If 4 is added...
Given:
The product of three consecutive terms of a geometric progression (G.P.) is 512.
To find:
The sum of the original three terms of the given G.P.
Solution:
Let the three consecutive terms of the G.P. be a/r, a, and ar, where 'a' is the first term and 'r' is the common ratio.
The product of these three terms is given by:
(a/r) * a * (ar) = 512
Simplifying the above expression, we get:
a^3 = 512
Taking the cube root on both sides, we get:
a = 8
So, the three terms of the G.P. are 8/r, 8, and 8r.
Adding 4 to the first and second terms:
The new terms become (8/r) + 4, 8 + 4, and 8r.
Forming an arithmetic progression (A.P.):
The three terms now form an arithmetic progression. This means that the difference between any two consecutive terms is constant.
The difference between the second and first term is:
(8 + 4) - ((8/r) + 4) = 8 - (8/r) = 8r - (8/r)
The difference between the third and second term is:
(8r) - (8 + 4) = 8r - 12
Since the difference between any two consecutive terms is constant, we equate the two expressions for the difference and solve for 'r':
8r - (8/r) = 8r - 12
Simplifying the above expression, we get:
8 - (8/r) = -12
Multiply both sides by 'r' to eliminate the fraction:
8r - 8 = -12r
Rearranging the terms, we get:
20r = 8
Dividing both sides by 20, we get:
r = 2/5
Substituting the value of 'r' back into the terms:
The three terms of the A.P. are (8/2/5) + 4, 8 + 4, and (8 * 2/5).
Simplifying the terms, we get:
(40/2) + 4, 12, and (16/5)
The sum of these three terms is:
(40/2) + 4 + 12 + (16/5) = 20 + 4 + 12 + (16/5) = 48 + (16/5)
Converting the mixed fraction to an improper fraction, we get:
48 + (16/5) = (240/5) + (16/5) = (240 + 16)/5 = 256/5
Therefore, the sum of the original three terms of the given G.P. is 256/5, which is approximately equal to 51.2.
Hence, option D is the correct answer.
The product of three consecutive terms of a geometric progression (G.P.) is 512.
To find:
The sum of the original three terms of the given G.P.
Solution:
Let the three consecutive terms of the G.P. be a/r, a, and ar, where 'a' is the first term and 'r' is the common ratio.
The product of these three terms is given by:
(a/r) * a * (ar) = 512
Simplifying the above expression, we get:
a^3 = 512
Taking the cube root on both sides, we get:
a = 8
So, the three terms of the G.P. are 8/r, 8, and 8r.
Adding 4 to the first and second terms:
The new terms become (8/r) + 4, 8 + 4, and 8r.
Forming an arithmetic progression (A.P.):
The three terms now form an arithmetic progression. This means that the difference between any two consecutive terms is constant.
The difference between the second and first term is:
(8 + 4) - ((8/r) + 4) = 8 - (8/r) = 8r - (8/r)
The difference between the third and second term is:
(8r) - (8 + 4) = 8r - 12
Since the difference between any two consecutive terms is constant, we equate the two expressions for the difference and solve for 'r':
8r - (8/r) = 8r - 12
Simplifying the above expression, we get:
8 - (8/r) = -12
Multiply both sides by 'r' to eliminate the fraction:
8r - 8 = -12r
Rearranging the terms, we get:
20r = 8
Dividing both sides by 20, we get:
r = 2/5
Substituting the value of 'r' back into the terms:
The three terms of the A.P. are (8/2/5) + 4, 8 + 4, and (8 * 2/5).
Simplifying the terms, we get:
(40/2) + 4, 12, and (16/5)
The sum of these three terms is:
(40/2) + 4 + 12 + (16/5) = 20 + 4 + 12 + (16/5) = 48 + (16/5)
Converting the mixed fraction to an improper fraction, we get:
48 + (16/5) = (240/5) + (16/5) = (240 + 16)/5 = 256/5
Therefore, the sum of the original three terms of the given G.P. is 256/5, which is approximately equal to 51.2.
Hence, option D is the correct answer.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer?
Question Description
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer?.
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer?.
Solutions for The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer?, a detailed solution for The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now from an A.P. Then the sum of the original three terms of the given G.P. isa)36b)24c)32d)48Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
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