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If the sum of n terms of an A.P. be 3n2 - n and its common difference is 6, then its first terms is:
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the sum of n terms of an A.P. be 3n2- n and its common difference i...
**Solution:**
Given that the sum of n terms of an A.P. is given by the formula:
Sn = n/2 [2a + (n-1)d]
where Sn is the sum of n terms, a is the first term, n is the number of terms, and d is the common difference.
In this case, we are given that Sn = 3n^2 - n and d = 6. We need to find the value of a.
Substituting the given values into the formula, we have:
3n^2 - n = n/2 [2a + (n-1)6]
Simplifying the equation:
3n^2 - n = n/2 [2a + 6n - 6]
Multiplying both sides by 2 to eliminate the fraction:
6n^2 - 2n = n [2a + 6n - 6]
Expanding the expression:
6n^2 - 2n = 2an + 6n^2 - 6n
Combining like terms:
6n^2 - 2n = 2an + 6n^2 - 6n
Rearranging the terms:
6n^2 + 6n^2 - 2n - 6n = 2an
Simplifying:
12n^2 - 8n = 2an
Dividing both sides by 2n to isolate a:
6n - 4 = a
Therefore, the first term a is equal to 6n - 4.
To find the value of a, we need to substitute n = 1 into the equation:
a = 6(1) - 4 = 6 - 4 = 2.
Hence, the correct answer is option 'A', a=2.
Given that the sum of n terms of an A.P. is given by the formula:
Sn = n/2 [2a + (n-1)d]
where Sn is the sum of n terms, a is the first term, n is the number of terms, and d is the common difference.
In this case, we are given that Sn = 3n^2 - n and d = 6. We need to find the value of a.
Substituting the given values into the formula, we have:
3n^2 - n = n/2 [2a + (n-1)6]
Simplifying the equation:
3n^2 - n = n/2 [2a + 6n - 6]
Multiplying both sides by 2 to eliminate the fraction:
6n^2 - 2n = n [2a + 6n - 6]
Expanding the expression:
6n^2 - 2n = 2an + 6n^2 - 6n
Combining like terms:
6n^2 - 2n = 2an + 6n^2 - 6n
Rearranging the terms:
6n^2 + 6n^2 - 2n - 6n = 2an
Simplifying:
12n^2 - 8n = 2an
Dividing both sides by 2n to isolate a:
6n - 4 = a
Therefore, the first term a is equal to 6n - 4.
To find the value of a, we need to substitute n = 1 into the equation:
a = 6(1) - 4 = 6 - 4 = 2.
Hence, the correct answer is option 'A', a=2.
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If the sum of n terms of an A.P. be 3n2- n and its common difference is 6, then its first terms is:a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer?
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If the sum of n terms of an A.P. be 3n2- n and its common difference is 6, then its first terms is:a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the sum of n terms of an A.P. be 3n2- n and its common difference is 6, then its first terms is:a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of n terms of an A.P. be 3n2- n and its common difference is 6, then its first terms is:a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer?.
If the sum of n terms of an A.P. be 3n2- n and its common difference is 6, then its first terms is:a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the sum of n terms of an A.P. be 3n2- n and its common difference is 6, then its first terms is:a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of n terms of an A.P. be 3n2- n and its common difference is 6, then its first terms is:a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer?.
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