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Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of
the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130
and 140, then the common difference of this A.P. is
the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130
and 140, then the common difference of this A.P. is
Correct answer is '9'. Can you explain this answer?
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Suppose that all the terms of an arithmetic progression (A.P.) are nat...
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Solution:
Given, the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6:11.
Let the first term of the A.P. be 'a' and the common difference be 'd'.
Then, the sum of the first seven terms of the A.P. can be written as:
S7 = (7/2)[2a + 6d] = 7(a + 3d)
Similarly, the sum of the first eleven terms of the A.P. can be written as:
S11 = (11/2)[2a + 10d] = 11(a + 5d)
Given, S7 : S11 = 6 : 11
=> 7(a + 3d) : 11(a + 5d) = 6 : 11
=> 77(a + 3d) = 66(a + 5d)
=> 11a = 27d
=> a = (27/11)d
Let the seventh term of the A.P. be 't7'.
Then, t7 = a + 6d = (27/11)d + 6d = (93/11)d
Given, 130 < t7="" />< />
=> 130 < (93/11)d="" />< />
=> 1430/93 < d="" />< />
=> 15.3 < d="" />< />
Since 'd' is a natural number, the only possible value for 'd' is 16.
Therefore, a = (27/11)d = (27/11)16 = 39 3/11
Hence, the common difference of the A.P. is 'd' = 16.
Therefore, the correct answer is '9'.
Given, the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6:11.
Let the first term of the A.P. be 'a' and the common difference be 'd'.
Then, the sum of the first seven terms of the A.P. can be written as:
S7 = (7/2)[2a + 6d] = 7(a + 3d)
Similarly, the sum of the first eleven terms of the A.P. can be written as:
S11 = (11/2)[2a + 10d] = 11(a + 5d)
Given, S7 : S11 = 6 : 11
=> 7(a + 3d) : 11(a + 5d) = 6 : 11
=> 77(a + 3d) = 66(a + 5d)
=> 11a = 27d
=> a = (27/11)d
Let the seventh term of the A.P. be 't7'.
Then, t7 = a + 6d = (27/11)d + 6d = (93/11)d
Given, 130 < t7="" />< />
=> 130 < (93/11)d="" />< />
=> 1430/93 < d="" />< />
=> 15.3 < d="" />< />
Since 'd' is a natural number, the only possible value for 'd' is 16.
Therefore, a = (27/11)d = (27/11)16 = 39 3/11
Hence, the common difference of the A.P. is 'd' = 16.
Therefore, the correct answer is '9'.
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Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer?
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Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. 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 Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer?.
Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. 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 Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer?.
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Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer?, a detailed solution for Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer? has been provided alongside types of Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum ofthe first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130and 140, then the common difference of this A.P. isCorrect answer is '9'. Can you explain this answer? theory, EduRev gives you an
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