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Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4.
Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.?
Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.?
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Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference ...
Understanding the Assertion and Reason
The assertion states that if the nth term of an arithmetic progression (AP) is given by 7 - 4n, then the common difference is -4. The reason provided explains how to find the common difference in an AP.
Assertion Analysis
- The nth term of an AP can be expressed as:
- a_n = a + (n-1)d
- Here, a is the first term, d is the common difference, and n is the term number.
- In the given expression, 7 - 4n, we can identify:
- a = 7 (when n = 1) and d = -4 (as it is the coefficient of n).
- Thus, the common difference d = -4.
Reason Analysis
- The reason correctly states how to determine the common difference:
- Common difference, d = a_(n+1) - a_n
- For an AP with terms derived from the nth term formula:
- a_n = 7 - 4n
- a_(n+1) = 7 - 4(n + 1) = 7 - 4n - 4 = 3 - 4n
- Therefore, d = (3 - 4n) - (7 - 4n) = 3 - 4n - 7 + 4n = -4.
Conclusion
- The assertion is true as the common difference is indeed -4.
- The reason is valid and supports the assertion, confirming that the method to find the common difference is correctly stated.
In summary, both the assertion and the reason hold true, establishing a solid understanding of the properties of an arithmetic progression.
The assertion states that if the nth term of an arithmetic progression (AP) is given by 7 - 4n, then the common difference is -4. The reason provided explains how to find the common difference in an AP.
Assertion Analysis
- The nth term of an AP can be expressed as:
- a_n = a + (n-1)d
- Here, a is the first term, d is the common difference, and n is the term number.
- In the given expression, 7 - 4n, we can identify:
- a = 7 (when n = 1) and d = -4 (as it is the coefficient of n).
- Thus, the common difference d = -4.
Reason Analysis
- The reason correctly states how to determine the common difference:
- Common difference, d = a_(n+1) - a_n
- For an AP with terms derived from the nth term formula:
- a_n = 7 - 4n
- a_(n+1) = 7 - 4(n + 1) = 7 - 4n - 4 = 3 - 4n
- Therefore, d = (3 - 4n) - (7 - 4n) = 3 - 4n - 7 + 4n = -4.
Conclusion
- The assertion is true as the common difference is indeed -4.
- The reason is valid and supports the assertion, confirming that the method to find the common difference is correctly stated.
In summary, both the assertion and the reason hold true, establishing a solid understanding of the properties of an arithmetic progression.
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Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4. Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.?
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Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4. Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4. Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4. Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.?.
Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4. Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4. Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sertion(A):If nth term of an AP is 7 – 4n ,then its common difference is −4. Reason(R):Common difference of an AP is given by d= 𝑎𝑛+1 − 𝑎𝑛.?.
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