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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : an - an - 1 is not independent of n then the given sequence is an AP.
Reason : Common difference d =an - an - 1 is constant or independent of n .
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'D'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) ...
We have, common difference of an AP
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d =an - an - 1 is independent of n or constant.
So, A is correct but R is incorrect.
Most Upvoted Answer
DIRECTION : In the following questions, a statement of assertion (A) ...
Algorithm
Step I. Obtain an
Step II. Replace n by (n - 1) is an to get an-1
Step III. Calculate an− an-1
Step IV. Check the value of an− an-1 .
If an− an-1 is independent of n, then the given
sequence is an A.P. Otherwise it is not an A.P
suppose an= 3-4n
put n=n-1
an-1=3-4(n-1)=3-4n+4
an-an-1=3-4n-3+4n-4 =-4 ( independent of n) so A is false.
common difference must be the same so it must be independent from 'n'
d=2n (never be considered because in this case d not remain the same)
Hence correct option is D
Step I. Obtain an
Step II. Replace n by (n - 1) is an to get an-1
Step III. Calculate an− an-1
Step IV. Check the value of an− an-1 .
If an− an-1 is independent of n, then the given
sequence is an A.P. Otherwise it is not an A.P
suppose an= 3-4n
put n=n-1
an-1=3-4(n-1)=3-4n+4
an-an-1=3-4n-3+4n-4 =-4 ( independent of n) so A is false.
common difference must be the same so it must be independent from 'n'
d=2n (never be considered because in this case d not remain the same)
Hence correct option is D
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DIRECTION : In the following questions, a statement of assertion (A) ...
Assertion (A): an - an-1 is not independent of n then the given sequence is an AP.
Reason (R): Common difference d = an - an-1 is constant or independent of n.
The correct answer is option 'D': Assertion (A) is false but reason (R) is true.
Explanation:
To determine whether the given sequence is an Arithmetic Progression (AP) or not, we need to consider the definition of an AP.
An Arithmetic Progression (AP) is a sequence in which the difference between any two consecutive terms is constant.
In other words, if the sequence follows the pattern a, a + d, a + 2d, a + 3d, ..., where 'a' is the first term and 'd' is the common difference, then it is an AP.
Now let's analyze the given assertion and reason:
Assertion (A): an - an-1 is not independent of n then the given sequence is an AP.
This assertion is not always true. The difference between any two consecutive terms, an - an-1, can vary with 'n'. It does not necessarily mean that the sequence is an AP.
For example, consider the sequence: 1, 4, 9, 16, 25, ...
Here, an - an-1 = (n^2) - (n-1)^2 = 2n - 1, which is not a constant value. But still, the sequence is not an AP because the difference between the terms is not constant.
Reason (R): Common difference d = an - an-1 is constant or independent of n.
This reason is true. In an AP, the common difference 'd' is constant and independent of 'n'. It means that the difference between any two consecutive terms remains the same throughout the sequence.
For example, consider the sequence: 2, 5, 8, 11, 14, ...
Here, an - an-1 = 3, which is a constant value. The sequence follows the AP pattern with a common difference of 3.
Therefore, the reason is true, but the assertion is false. The given sequence cannot be considered an AP solely based on the fact that an - an-1 is not independent of 'n'. The key factor in determining an AP is the constancy of the difference between consecutive terms.
Reason (R): Common difference d = an - an-1 is constant or independent of n.
The correct answer is option 'D': Assertion (A) is false but reason (R) is true.
Explanation:
To determine whether the given sequence is an Arithmetic Progression (AP) or not, we need to consider the definition of an AP.
An Arithmetic Progression (AP) is a sequence in which the difference between any two consecutive terms is constant.
In other words, if the sequence follows the pattern a, a + d, a + 2d, a + 3d, ..., where 'a' is the first term and 'd' is the common difference, then it is an AP.
Now let's analyze the given assertion and reason:
Assertion (A): an - an-1 is not independent of n then the given sequence is an AP.
This assertion is not always true. The difference between any two consecutive terms, an - an-1, can vary with 'n'. It does not necessarily mean that the sequence is an AP.
For example, consider the sequence: 1, 4, 9, 16, 25, ...
Here, an - an-1 = (n^2) - (n-1)^2 = 2n - 1, which is not a constant value. But still, the sequence is not an AP because the difference between the terms is not constant.
Reason (R): Common difference d = an - an-1 is constant or independent of n.
This reason is true. In an AP, the common difference 'd' is constant and independent of 'n'. It means that the difference between any two consecutive terms remains the same throughout the sequence.
For example, consider the sequence: 2, 5, 8, 11, 14, ...
Here, an - an-1 = 3, which is a constant value. The sequence follows the AP pattern with a common difference of 3.
Therefore, the reason is true, but the assertion is false. The given sequence cannot be considered an AP solely based on the fact that an - an-1 is not independent of 'n'. The key factor in determining an AP is the constancy of the difference between consecutive terms.
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?.
Solutions for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : an - an - 1 is not independent of n then the given sequence is an AP.Reason : Common difference d =an - an - 1 is constant or independent of n .a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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