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If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term is
- a)2
- b)3
- c)4
- d)1
Correct answer is option 'A'. Can you explain this answer?
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If the sum of first n terms of an A.P. be 3n2 - n and its common diffe...
Given information:
- Sum of first n terms of an A.P. = 3n^2 - n
- Common difference (d) = 6
Formula for the sum of n terms of an A.P.:
- Sum of n terms = n/2 [2a + (n-1)d]
Using the given sum formula:
- 3n^2 - n = n/2 [2a + (n-1)6]
- 3n^2 - n = n/2 [2a + 6n - 6]
- 3n^2 - n = n [a + 3n - 3]
- 3n^2 - n = an + 3n^2 - 3n
- 2n^2 = an
Calculating the first term (a):
- Substituting d = 6 into the formula a = 2n
- a = 2n = 2(1) = 2
Therefore, the first term of the arithmetic progression is 2. So, the correct answer is option 'A'.
- Sum of first n terms of an A.P. = 3n^2 - n
- Common difference (d) = 6
Formula for the sum of n terms of an A.P.:
- Sum of n terms = n/2 [2a + (n-1)d]
Using the given sum formula:
- 3n^2 - n = n/2 [2a + (n-1)6]
- 3n^2 - n = n/2 [2a + 6n - 6]
- 3n^2 - n = n [a + 3n - 3]
- 3n^2 - n = an + 3n^2 - 3n
- 2n^2 = an
Calculating the first term (a):
- Substituting d = 6 into the formula a = 2n
- a = 2n = 2(1) = 2
Therefore, the first term of the arithmetic progression is 2. So, the correct answer is option 'A'.
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If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term isa)2b)3c)4d)1Correct answer is option 'A'. Can you explain this answer?
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If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term isa)2b)3c)4d)1Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term isa)2b)3c)4d)1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of first n terms of an A.P. be 3n2 - n and its common difference is 6, then its first term isa)2b)3c)4d)1Correct answer is option 'A'. Can you explain this answer?.
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