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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.
Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1
- a)Both A and R are true and R is the correct explanation for A.
- b)Both A and R are true and R is not correct explanation for A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
To verify the reason, we are given Sn = 3n2 – 4n
Then, an – 1 = 3(n – 1)2 – 4(n – 1)
= 3n2 + 3 – 6n – 4n + 4 = 3n2 – 10n + 7
an = Sn – Sn – 1an = 3n2 – 4n – (3n2 – 10n + 7) = 6n – 7
Reason is correct.
Therefore, Both A and R are true and R is the correct explanation for A.
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Directions: In the following questions, A statement of Assertion (A) ...
Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n^2 – 4n.
Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1.
To understand this question, let's break it down into two parts: the assertion and the reason.
Assertion: The sum of the first n terms of an arithmetic progression (A.P) is given by Sn = 3n^2 – 4n.
To find the sum of the first n terms of an A.P, we use the formula Sn = (n/2)(2a + (n-1)d), where a is the first term and d is the common difference.
Comparing this formula with Sn = 3n^2 – 4n, we can see that the first term (a) is equal to -4 and the common difference (d) is equal to 8. Therefore, the first term of the A.P is -4 and the common difference is 8.
Reason: The nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn-1.
To find the nth term of an A.P, we can use the formula an = a + (n-1)d, where a is the first term and d is the common difference.
Using the values of a = -4 and d = 8 from the assertion, we can calculate the nth term as an = -4 + (n-1)(8) = -4 + 8n - 8 = 8n - 12.
Comparing this with the given expression for the nth term, an = 6n - 7, we can see that it is not the same. Therefore, the reason is incorrect.
Conclusion: Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion. Therefore, the correct answer is option 'A' - Both A and R are true and R is not the correct explanation for A.
Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1.
To understand this question, let's break it down into two parts: the assertion and the reason.
Assertion: The sum of the first n terms of an arithmetic progression (A.P) is given by Sn = 3n^2 – 4n.
To find the sum of the first n terms of an A.P, we use the formula Sn = (n/2)(2a + (n-1)d), where a is the first term and d is the common difference.
Comparing this formula with Sn = 3n^2 – 4n, we can see that the first term (a) is equal to -4 and the common difference (d) is equal to 8. Therefore, the first term of the A.P is -4 and the common difference is 8.
Reason: The nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn-1.
To find the nth term of an A.P, we can use the formula an = a + (n-1)d, where a is the first term and d is the common difference.
Using the values of a = -4 and d = 8 from the assertion, we can calculate the nth term as an = -4 + (n-1)(8) = -4 + 8n - 8 = 8n - 12.
Comparing this with the given expression for the nth term, an = 6n - 7, we can see that it is not the same. Therefore, the reason is incorrect.
Conclusion: Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion. Therefore, the correct answer is option 'A' - Both A and R are true and R is not the correct explanation for A.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but 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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Here you can find the meaning of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The sum of first n terms of an A.P is given by Sn = 3n2 – 4n. Then its n term is given by the term an = 6n – 7.Reason (R): nth term of an A.P, whose sum to n terms is Sn, is given by an = Sn – Sn – 1a)Both A and R are true and R is the correct explanation for A.b)Both A and R are true and R is not correct explanation for A.c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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