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The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans?
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The mth term of an A.P is n and nth term is m. The rth term of it is??...
Explanation:
- Given Information:
- The mth term of an A.P is n
- The nth term of the A.P is m
- Formula for nth term of an Arithmetic Progression (A.P):
- The nth term of an A.P is given by: a + (n-1)d
- Where 'a' is the first term, 'n' is the position of the term, and 'd' is the common difference
- Using the Given Information:
- From the first point, we know that the mth term of the A.P is n
- Therefore, the mth term can be represented as: a + (m-1)d = n --> (1)
- From the second point, we know that the nth term of the A.P is m
- Therefore, the nth term can be represented as: a + (n-1)d = m --> (2)
- Finding the rth term of the A.P:
- To find the rth term of the A.P, we need to substitute the values of 'a' and 'd' from equations (1) and (2) into the formula for the nth term
- Subtracting equation (1) from equation (2), we get: (n-1)d - (m-1)d = m - n
- Simplifying, we get: (n - m)d = m - n
- Solving for 'd', we get: d = (m - n) / (n - m) = -1
- Substituting 'd = -1' back into equation (1), we get: a - (m-1) = n --> a = n + m - 1
- Final Answer:
- Therefore, the rth term of the A.P is given by: a + (r-1)d = (n + m - 1) + (r-1)(-1) = n + m - r
- Given Information:
- The mth term of an A.P is n
- The nth term of the A.P is m
- Formula for nth term of an Arithmetic Progression (A.P):
- The nth term of an A.P is given by: a + (n-1)d
- Where 'a' is the first term, 'n' is the position of the term, and 'd' is the common difference
- Using the Given Information:
- From the first point, we know that the mth term of the A.P is n
- Therefore, the mth term can be represented as: a + (m-1)d = n --> (1)
- From the second point, we know that the nth term of the A.P is m
- Therefore, the nth term can be represented as: a + (n-1)d = m --> (2)
- Finding the rth term of the A.P:
- To find the rth term of the A.P, we need to substitute the values of 'a' and 'd' from equations (1) and (2) into the formula for the nth term
- Subtracting equation (1) from equation (2), we get: (n-1)d - (m-1)d = m - n
- Simplifying, we get: (n - m)d = m - n
- Solving for 'd', we get: d = (m - n) / (n - m) = -1
- Substituting 'd = -1' back into equation (1), we get: a - (m-1) = n --> a = n + m - 1
- Final Answer:
- Therefore, the rth term of the A.P is given by: a + (r-1)d = (n + m - 1) + (r-1)(-1) = n + m - r
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The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans?
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The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans? 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 The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans?.
The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans? 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 The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mth term of an A.P is n and nth term is m. The rth term of it is??? Ans is m n-r .can anyone explain this ans?.
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