CAT Exam > CAT Questions > The sum of n terms of an A.P. is given by (5n...
Start Learning for Free
The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?
- a)11
- b)13
- c)15
- d)17
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will ...
Let sum of 4 terms and sum of 5 terms be S4 and S5 respectively.
S5 = [5(5)2 + 7(5) + 4]/4 = 41
S5 = [5(5)2 + 7(5) + 4]/4 = 41
S4 = [5(4)2 + 7(4) + 4]/4 = 28
5th term of an A.P. = S5 - S4 = 13
5th term of an A.P. = S5 - S4 = 13
Hence, option 2.
Free Test
FREE
| Start Free Test |
Community Answer
The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will ...
To find the fifth term of an arithmetic progression (A.P.), we need to use the formula for the sum of the first n terms of an A.P.:
Sn = (n/2)(2a + (n-1)d)
Where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Given that the sum of the first n terms is (5n^2 + 7n + 4)/4, we can equate this expression to Sn:
(5n^2 + 7n + 4)/4 = (n/2)(2a + (n-1)d)
Simplifying this equation, we get:
5n^2 + 7n + 4 = n(2a + (n-1)d)
Expanding the right side, we have:
5n^2 + 7n + 4 = 2an + nd - d
Rearranging the terms, we get:
5n^2 + (7 - 2a)n + (4 + d) = 0
This is a quadratic equation in terms of n. Since it is given that this equation is true for all n, the coefficient of n^2 must be zero. Therefore, we have:
5 = 0
This is not possible, so there must be an error in the given equation for the sum of the first n terms. Without the correct equation, we cannot determine the fifth term of the A.P.
Sn = (n/2)(2a + (n-1)d)
Where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
Given that the sum of the first n terms is (5n^2 + 7n + 4)/4, we can equate this expression to Sn:
(5n^2 + 7n + 4)/4 = (n/2)(2a + (n-1)d)
Simplifying this equation, we get:
5n^2 + 7n + 4 = n(2a + (n-1)d)
Expanding the right side, we have:
5n^2 + 7n + 4 = 2an + nd - d
Rearranging the terms, we get:
5n^2 + (7 - 2a)n + (4 + d) = 0
This is a quadratic equation in terms of n. Since it is given that this equation is true for all n, the coefficient of n^2 must be zero. Therefore, we have:
5 = 0
This is not possible, so there must be an error in the given equation for the sum of the first n terms. Without the correct equation, we cannot determine the fifth term of the A.P.
|
Explore Courses for CAT exam
|
|
Top Courses for CATView all
Question Description
The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct 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 sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct 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 sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct answer is option 'B'. Can you explain this answer?.
The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct 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 sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct 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 sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct answer is option 'B'. Can you explain this answer?.
Solutions for The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct 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 sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The sum of n terms of an A.P. is given by (5n2 + 7n + 4)/4. What will be the fifth term of this A.P?a)11b)13c)15d)17Correct 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 on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily