Defence Exam > Defence Questions > The fifth term of an AP of n terms, whose sum...
Start Learning for Free
The fifth term of an AP of n terms, whose sum is n2 + n, is
- a)5
- b)7
- c)8
- d)15
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)1...
Most Upvoted Answer
The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)1...
Explanation:
Given information:
The sum of the n terms of an arithmetic progression (AP) is n^2 + n.
To find:
The fifth term of the AP.
Solution:
Step 1: Finding the sum of the n terms of the AP
The sum of n terms of an AP is given by the formula:
Sum = n/2 [2a + (n-1)d]
Given that the sum of the n terms is n^2 + n, we can write:
n^2 + n = n/2 [2a + (n-1)d]
2n^2 + 2n = n[2a + (n-1)d]
2n^2 + 2n = 2an + n^2 - nd
n^2 + 3n = 2an - nd
Step 2: Finding the fifth term of the AP
Let the first term of the AP be 'a' and the common difference be 'd'.
The nth term of an AP is given by the formula:
Tn = a + (n-1)d
Given that the sum of the n terms is n^2 + n, we have:
n^2 + 3n = 2an - nd
Substitute n = 5 into the above equation to find the fifth term of the AP:
5^2 + 3(5) = 2a(5) - 5d
25 + 15 = 10a - 5d
40 = 10a - 5d
8 = 2a - d
Hence, the fifth term of the AP is 2a - d = 2(8) - 1 = 15.
Therefore, the correct answer is option B) 15.
Given information:
The sum of the n terms of an arithmetic progression (AP) is n^2 + n.
To find:
The fifth term of the AP.
Solution:
Step 1: Finding the sum of the n terms of the AP
The sum of n terms of an AP is given by the formula:
Sum = n/2 [2a + (n-1)d]
Given that the sum of the n terms is n^2 + n, we can write:
n^2 + n = n/2 [2a + (n-1)d]
2n^2 + 2n = n[2a + (n-1)d]
2n^2 + 2n = 2an + n^2 - nd
n^2 + 3n = 2an - nd
Step 2: Finding the fifth term of the AP
Let the first term of the AP be 'a' and the common difference be 'd'.
The nth term of an AP is given by the formula:
Tn = a + (n-1)d
Given that the sum of the n terms is n^2 + n, we have:
n^2 + 3n = 2an - nd
Substitute n = 5 into the above equation to find the fifth term of the AP:
5^2 + 3(5) = 2a(5) - 5d
25 + 15 = 10a - 5d
40 = 10a - 5d
8 = 2a - d
Hence, the fifth term of the AP is 2a - d = 2(8) - 1 = 15.
Therefore, the correct answer is option B) 15.
|
Explore Courses for Defence exam
|
|
The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer?
Question Description
The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer?.
The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer?.
Solutions for The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The fifth term of an AP of n terms, whose sum is n2+ n, isa)5b)7c)8d)15Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence 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