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In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is?
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In an arithmetic progression, the seventh term is x, and (x+7)th term ...
Given Information:
- Seventh term in the arithmetic progression is x.
- (x+7)th term in the arithmetic progression is 0.
Calculating the Common Difference:
- Let the first term of the arithmetic progression be 'a' and the common difference be 'd'.
- The seventh term can be expressed as: a + 6d = x
- The (x+7)th term can be expressed as: a + (x+6)d = 0
Solving the Equations:
- Substitute x = a + 6d in the second equation: a + (a + 6d + 6)d = 0
- Simplifying the equation: 2a + 12d + 6d = 0
- Further simplification: 2a + 18d = 0
- Dividing the equation by 2: a + 9d = 0
Calculating the xth term:
- Substitute a + 6d = x in the equation a + 9d = 0: x - 3d = 0
- Solving for x: x = 3d
Therefore, the xth term in the arithmetic progression is 3d.
- Seventh term in the arithmetic progression is x.
- (x+7)th term in the arithmetic progression is 0.
Calculating the Common Difference:
- Let the first term of the arithmetic progression be 'a' and the common difference be 'd'.
- The seventh term can be expressed as: a + 6d = x
- The (x+7)th term can be expressed as: a + (x+6)d = 0
Solving the Equations:
- Substitute x = a + 6d in the second equation: a + (a + 6d + 6)d = 0
- Simplifying the equation: 2a + 12d + 6d = 0
- Further simplification: 2a + 18d = 0
- Dividing the equation by 2: a + 9d = 0
Calculating the xth term:
- Substitute a + 6d = x in the equation a + 9d = 0: x - 3d = 0
- Solving for x: x = 3d
Therefore, the xth term in the arithmetic progression is 3d.
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In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is?
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In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is?.
In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an arithmetic progression, the seventh term is x, and (x+7)th term is zero. Then xth term is?.
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