CAT Exam > CAT Questions > The difference between the third and first t...
Start Learning for Free
The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.
- a)6
- b)7
- c)9
- d)10
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The difference between the third and first terms of a GP is 3. If the...
First, let's denote the first term of the GP as 'a' and the common ratio as 'r'.
- Given Information:
The difference between the third and first terms of the GP is 3. This can be expressed as:
ar^2 - a = 3
- Using the formula for the terms of a GP:
The third term of the GP can be expressed as ar^2, and the first term as a.
So, ar^2 - a = 3 can be rewritten as ar^2 = a + 3
- Since both 'a' and 'r' are positive integers:
We can assume 'a = 1' and 'r = 2' to fulfill the condition above.
Therefore, the GP becomes 1, 2, 4.
- Sum of the first three terms:
The sum of the first three terms of a GP is given by:
Sum = a(1 - r^3) / (1 - r)
Plugging in the values of 'a' and 'r', we get:
Sum = 1(1 - 2^3) / (1 - 2) = 1(1 - 8) / -1 = -7 / -1 = 7
Therefore, the sum of the first three terms of the progression is 7, which corresponds to option 'B'.
- Given Information:
The difference between the third and first terms of the GP is 3. This can be expressed as:
ar^2 - a = 3
- Using the formula for the terms of a GP:
The third term of the GP can be expressed as ar^2, and the first term as a.
So, ar^2 - a = 3 can be rewritten as ar^2 = a + 3
- Since both 'a' and 'r' are positive integers:
We can assume 'a = 1' and 'r = 2' to fulfill the condition above.
Therefore, the GP becomes 1, 2, 4.
- Sum of the first three terms:
The sum of the first three terms of a GP is given by:
Sum = a(1 - r^3) / (1 - r)
Plugging in the values of 'a' and 'r', we get:
Sum = 1(1 - 2^3) / (1 - 2) = 1(1 - 8) / -1 = -7 / -1 = 7
Therefore, the sum of the first three terms of the progression is 7, which corresponds to option 'B'.
Free Test
FREE
| Start Free Test |
Community Answer
The difference between the third and first terms of a GP is 3. If the...
Let the 3 terms of the GP be a, ar and ar2.
Given: ar2 – a = 3
a(r2 – 1) = 3
a(r + 1)(r – 1) = 3
Since ‘a’ and ‘r’ are positive integers,
⇒ a = 1 and r = 2
So, the numbers are 1, 2 and 4.
Sum = 1 + 2 + 4 = 7
|
Explore Courses for CAT exam
|
|
Similar CAT Doubts
Top Courses for CATView all
The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer?
Question Description
The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer?.
The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer?.
Solutions for The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The difference between the third and first terms of a GP is 3. If the first term and the common ratio of the GP are positive integers, then find the sum of the first three terms of the progression.a)6b)7c)9d)10Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice CAT tests.
|
|
Explore Courses for CAT 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