JEE Exam > JEE Questions > If a, b, c are in A.P., thena)b - a = b - cb)...
Start Learning for Free
If a, b, c are in A.P., then
- a)b - a = b - c
- b)b is the arithmetic mean of a and c.
- c)2a = b + c
- d)a - b = c - b
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean ...
If a, b, c are in A.P., then b is the arithmetic mean of a and c.
a b and c are in AP.
∴ b - a = c - b
⇒ 2b = a + c ........ (1)
The arithmetic mean of a and c
= (a+c)/2
Using equation (1), we get
= 2b/2
= b
∴ The arithmetic mean of a and c = b
Thus, the arithmetic mean of a and c is b.
a b and c are in AP.
∴ b - a = c - b
⇒ 2b = a + c ........ (1)
The arithmetic mean of a and c
= (a+c)/2
Using equation (1), we get
= 2b/2
= b
∴ The arithmetic mean of a and c = b
Thus, the arithmetic mean of a and c is b.
Free Test
FREE
| Start Free Test |
Community Answer
If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean ...
Understanding Arithmetic Progression (A.P.)
When three numbers a, b, and c are in Arithmetic Progression (A.P.), it means they have a specific relationship. A.P. is characterized by a constant difference between consecutive terms.
Key Definition
- In A.P., the middle term is the average of the two outer terms. Hence, for numbers a, b, and c:
- b = (a + c) / 2
This implies that b is the arithmetic mean of a and c.
Analyzing the Options
Let's break down each option to see their validity:
- Option a) b - a = b - c
This implies a + c = 2b, which is true.
- Option b) b is the arithmetic mean of a and c
This directly aligns with the definition of A.P., making it correct.
- Option c) 2a = b + c
Rearranging gives b = 2a - c. This is not a general rule for A.P.
- Option d) a - b = c - b
Rearranging gives a + c = 2b, which is true but doesn't define A.P. directly.
Conclusion
The correct answer is Option b) because it succinctly captures the essence of A.P., where b is indeed the arithmetic mean of a and c. This fundamental property is central to understanding and solving problems related to Arithmetic Progression.
In summary, when a, b, and c are in A.P., b perfectly represents the mean of the outer terms a and c, confirming that Option b is the correct choice.
When three numbers a, b, and c are in Arithmetic Progression (A.P.), it means they have a specific relationship. A.P. is characterized by a constant difference between consecutive terms.
Key Definition
- In A.P., the middle term is the average of the two outer terms. Hence, for numbers a, b, and c:
- b = (a + c) / 2
This implies that b is the arithmetic mean of a and c.
Analyzing the Options
Let's break down each option to see their validity:
- Option a) b - a = b - c
This implies a + c = 2b, which is true.
- Option b) b is the arithmetic mean of a and c
This directly aligns with the definition of A.P., making it correct.
- Option c) 2a = b + c
Rearranging gives b = 2a - c. This is not a general rule for A.P.
- Option d) a - b = c - b
Rearranging gives a + c = 2b, which is true but doesn't define A.P. directly.
Conclusion
The correct answer is Option b) because it succinctly captures the essence of A.P., where b is indeed the arithmetic mean of a and c. This fundamental property is central to understanding and solving problems related to Arithmetic Progression.
In summary, when a, b, and c are in A.P., b perfectly represents the mean of the outer terms a and c, confirming that Option b is the correct choice.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. 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 If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer?.
If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. 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 If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer?.
Solutions for If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. 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 If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If a, b, c are in A.P., thena)b - a = b - cb)b is the arithmetic mean of a and c.c)2a = b + cd)a - b = c - bCorrect answer is option 'B'. 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 on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily