Quant Exam > Quant Questions > Find the second term of an AP if the sum of i...
Start Learning for Free
Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.
- a)–3
- b)–2
- c)–1
- d)0
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Find the second term of an AP if the sum of its first five even terms ...
Since the sum of the first five even terms is 15, we have that the 2nd, 4th, 6th, 8th and 10th term of
the AP should add up to 15. We also need to understand that these 5 terms of the AP would also be
in an AP by themselves and hence, the value of the 6th term (being the middle term of the AP)
would be the average of 15 over 5 terms. Thus, the value of the 6th term is 3. Also, since the sum
of the first three terms of the AP is –3, we get that the 2nd term would have a value of –1. Thus, the
AP can be visualized as:
_, -1, _,_,_,3,….
Thus, it is obvious that the AP would be –2, –1, 0, 1, 2, 3. The second term is –1. Thus, option (c)
is correct.
the AP should add up to 15. We also need to understand that these 5 terms of the AP would also be
in an AP by themselves and hence, the value of the 6th term (being the middle term of the AP)
would be the average of 15 over 5 terms. Thus, the value of the 6th term is 3. Also, since the sum
of the first three terms of the AP is –3, we get that the 2nd term would have a value of –1. Thus, the
AP can be visualized as:
_, -1, _,_,_,3,….
Thus, it is obvious that the AP would be –2, –1, 0, 1, 2, 3. The second term is –1. Thus, option (c)
is correct.
Most Upvoted Answer
Find the second term of an AP if the sum of its first five even terms ...
Given information:
- Sum of first five even terms of an AP = 15
- Sum of first three terms of the same AP = 3
To find: Second term of the AP
Solution:
Let the first term of the AP be 'a' and the common difference be 'd'.
We know that the sum of first five even terms of an AP is given by:
Sum of first five even terms = 2(a+2d) + 2(a+4d) + 2(a+6d) = 6a + 24d
From the given information, we have:
6a + 24d = 15 ---(1)
We also know that the sum of first three terms of the same AP is given by:
Sum of first three terms = a + (a+d) + (a+2d) = 3a + 3d
From the given information, we have:
3a + 3d = 3 ---(2)
Dividing equation (1) by 6, we get:
a + 4d = 5/2
Subtracting equation (2) from the above equation, we get:
d = -1/2
Substituting d = -1/2 in equation (2), we get:
3a - 3/2 = 3
3a = 9/2
a = 3/2
Therefore, the second term of the AP is given by:
a + d = 3/2 - 1/2 = 1
Hence, option (c) is the correct answer.
- Sum of first five even terms of an AP = 15
- Sum of first three terms of the same AP = 3
To find: Second term of the AP
Solution:
Let the first term of the AP be 'a' and the common difference be 'd'.
We know that the sum of first five even terms of an AP is given by:
Sum of first five even terms = 2(a+2d) + 2(a+4d) + 2(a+6d) = 6a + 24d
From the given information, we have:
6a + 24d = 15 ---(1)
We also know that the sum of first three terms of the same AP is given by:
Sum of first three terms = a + (a+d) + (a+2d) = 3a + 3d
From the given information, we have:
3a + 3d = 3 ---(2)
Dividing equation (1) by 6, we get:
a + 4d = 5/2
Subtracting equation (2) from the above equation, we get:
d = -1/2
Substituting d = -1/2 in equation (2), we get:
3a - 3/2 = 3
3a = 9/2
a = 3/2
Therefore, the second term of the AP is given by:
a + d = 3/2 - 1/2 = 1
Hence, option (c) is the correct answer.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer?
Question Description
Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer?.
Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer?.
Solutions for Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to –3.a)–3b)–2c)–1d)0Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup