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If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59, 6 . . . , then what is the value of nl
- a)7
- b)9
- c)11
- d)13
Correct answer is option 'C'. Can you explain this answer?
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Given, the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59, 61...
Let the nth term of the first AP be a and the common difference be d. Therefore,
First AP: a = 2, d = 3
The sum of the first 2n terms of the first AP is given by:
S1 = n/2[2a + (2n - 1)d]
S1 = n/2[2(2) + (2n - 1)3]
S1 = 3n^2
Let the nth term of the second AP be b and the common difference be c. Therefore,
Second AP: b = 57, c = 2
The sum of the first n terms of the second AP is given by:
S2 = n/2[2b + (n - 1)c]
S2 = n/2[2(57) + (n - 1)2]
S2 = 29n + n^2
According to the question, S1 = S2
3n^2 = 29n + n^2
2n^2 - 29n = 0
n(2n - 29) = 0
n = 0 or n = 29/2
Since n cannot be 0, we get n = 29/2 which is not an integer.
Therefore, there is no solution for n and the question is incorrect.
Hence, the correct answer cannot be determined.
Let the nth term of the first AP be a and the common difference be d. Therefore,
First AP: a = 2, d = 3
The sum of the first 2n terms of the first AP is given by:
S1 = n/2[2a + (2n - 1)d]
S1 = n/2[2(2) + (2n - 1)3]
S1 = 3n^2
Let the nth term of the second AP be b and the common difference be c. Therefore,
Second AP: b = 57, c = 2
The sum of the first n terms of the second AP is given by:
S2 = n/2[2b + (n - 1)c]
S2 = n/2[2(57) + (n - 1)2]
S2 = 29n + n^2
According to the question, S1 = S2
3n^2 = 29n + n^2
2n^2 - 29n = 0
n(2n - 29) = 0
n = 0 or n = 29/2
Since n cannot be 0, we get n = 29/2 which is not an integer.
Therefore, there is no solution for n and the question is incorrect.
Hence, the correct answer cannot be determined.
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If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59,6 . . . , then what is the value of nla)7b)9c)11d)13Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59,6 . . . , then what is the value of nla)7b)9c)11d)13Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59,6 . . . , then what is the value of nla)7b)9c)11d)13Correct answer is option 'C'. Can you explain this answer?.
If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59,6 . . . , then what is the value of nla)7b)9c)11d)13Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59,6 . . . , then what is the value of nla)7b)9c)11d)13Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the first 2n terms of the AP 2, 5, 8... is equal to the sum of first n terms of the AP 57, 59,6 . . . , then what is the value of nla)7b)9c)11d)13Correct answer is option 'C'. Can you explain this answer?.
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