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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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.
Reason : Common difference of an A.P. is given by d =an + 1 - an
- 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 'A'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) ...
Both are correct. Reason is the correct explanation.
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Assertion, an = 7 - 4n
d = an + 1 -an
= 7 - 4 (n + 1) - 7 (-4n)
= 7 - 4n - 4 - 7 + 4n = - 4
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DIRECTION : In the following questions, a statement of assertion (A) ...
Assertion: If the nth term of an A.P. is 7 - 4n, then its common difference is -4.
Reason: Common difference of an A.P. is given by d = a(n+1) - an
Explanation:
An Arithmetic Progression (A.P.) is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is known as the common difference.
To determine whether the assertion and reason are true or false, we need to evaluate each statement separately.
Assertion: If the nth term of an A.P. is 7 - 4n, then its common difference is -4.
To find the common difference, we can subtract the (n-1)th term from the nth term. Let's calculate the difference:
(n)th term = 7 - 4n
(n-1)th term = 7 - 4(n-1) = 7 - 4n + 4 = 11 - 4n
Common difference = (n)th term - (n-1)th term
= (7 - 4n) - (11 - 4n)
= 7 - 4n - 11 + 4n
= -4
So, the common difference is indeed -4. Therefore, the assertion is true.
Reason: Common difference of an A.P. is given by d = a(n+1) - an
The formula mentioned in the reason is incorrect. The correct formula for the common difference of an A.P. is:
d = a(n+1) - an
where 'd' is the common difference, 'a(n+1)' is the (n+1)th term, and 'an' is the nth term.
In this case, the formula would be:
d = (7 - 4(n+1)) - (7 - 4n)
= 7 - 4n - 4 - 4n - 7 + 4n
= 4n - 4n - 4 - 7
= -11
The calculated value of the common difference using the given formula is -11, which is different from the actual common difference of -4.
Therefore, the reason is false.
Conclusion:
Both the assertion and reason are true, but the reason is not the correct explanation of the assertion. The reason provides an incorrect formula for the common difference of an A.P. Hence, the correct answer is option 'B' - Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).
Reason: Common difference of an A.P. is given by d = a(n+1) - an
Explanation:
An Arithmetic Progression (A.P.) is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is known as the common difference.
To determine whether the assertion and reason are true or false, we need to evaluate each statement separately.
Assertion: If the nth term of an A.P. is 7 - 4n, then its common difference is -4.
To find the common difference, we can subtract the (n-1)th term from the nth term. Let's calculate the difference:
(n)th term = 7 - 4n
(n-1)th term = 7 - 4(n-1) = 7 - 4n + 4 = 11 - 4n
Common difference = (n)th term - (n-1)th term
= (7 - 4n) - (11 - 4n)
= 7 - 4n - 11 + 4n
= -4
So, the common difference is indeed -4. Therefore, the assertion is true.
Reason: Common difference of an A.P. is given by d = a(n+1) - an
The formula mentioned in the reason is incorrect. The correct formula for the common difference of an A.P. is:
d = a(n+1) - an
where 'd' is the common difference, 'a(n+1)' is the (n+1)th term, and 'an' is the nth term.
In this case, the formula would be:
d = (7 - 4(n+1)) - (7 - 4n)
= 7 - 4n - 4 - 4n - 7 + 4n
= 4n - 4n - 4 - 7
= -11
The calculated value of the common difference using the given formula is -11, which is different from the actual common difference of -4.
Therefore, the reason is false.
Conclusion:
Both the assertion and reason are true, but the reason is not the correct explanation of the assertion. The reason provides an incorrect formula for the common difference of an A.P. Hence, the correct answer is option 'B' - Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).
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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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. 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 : If n th term of an A.P. is 7 -4n , then its common differences is -4.Reason : Common difference of an A.P. is given by d =an + 1 - ana)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 'A'. Can you explain this answer? theory, EduRev gives you an
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