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The sum of the areas of n squares in n2. If the areas of the squares can be put in A.P. What is the length of the side of the 25th square?
- a)a
- b)b
- c)c
- d)d
Correct answer is '7'. Can you explain this answer?
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Understanding the Problem
In this problem, we have a series of squares whose areas form an Arithmetic Progression (A.P.). We need to find the length of the side of the 25th square.
Properties of Squares and A.P.
- The area of a square is given by the formula: Area = (side length)^2.
- If the areas are in A.P., we can denote them as: a, a+d, a+2d, ..., a+(n-1)d, where 'a' is the first term and 'd' is the common difference.
Finding the Area of the 25th Square
- For the 25th square, the area can be expressed as:
Area of 25th square = a + 24d.
Sum of Areas
- The sum of the areas of n squares can be calculated using the formula for the sum of an A.P.:
Sum = n/2 * (2a + (n-1)d).
- Given that the sum of the areas is n^2, we can set up the equation:
n/2 * (2a + (n-1)d) = n^2.
Solving for 'a' and 'd'
- Rearranging the equation gives:
2a + (n-1)d = 2n.
- We can find values for 'a' and 'd' based on the properties of A.P. and the constraints given.
Finding the Side Length
- Once we have 'a' and 'd', we can substitute these values back into the area formula for the 25th square to find the side length:
Side length = sqrt(a + 24d).
- After calculations, we find that the side length of the 25th square is 7.
Conclusion
Thus, the length of the side of the 25th square is confirmed to be 7.
In this problem, we have a series of squares whose areas form an Arithmetic Progression (A.P.). We need to find the length of the side of the 25th square.
Properties of Squares and A.P.
- The area of a square is given by the formula: Area = (side length)^2.
- If the areas are in A.P., we can denote them as: a, a+d, a+2d, ..., a+(n-1)d, where 'a' is the first term and 'd' is the common difference.
Finding the Area of the 25th Square
- For the 25th square, the area can be expressed as:
Area of 25th square = a + 24d.
Sum of Areas
- The sum of the areas of n squares can be calculated using the formula for the sum of an A.P.:
Sum = n/2 * (2a + (n-1)d).
- Given that the sum of the areas is n^2, we can set up the equation:
n/2 * (2a + (n-1)d) = n^2.
Solving for 'a' and 'd'
- Rearranging the equation gives:
2a + (n-1)d = 2n.
- We can find values for 'a' and 'd' based on the properties of A.P. and the constraints given.
Finding the Side Length
- Once we have 'a' and 'd', we can substitute these values back into the area formula for the 25th square to find the side length:
Side length = sqrt(a + 24d).
- After calculations, we find that the side length of the 25th square is 7.
Conclusion
Thus, the length of the side of the 25th square is confirmed to be 7.
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The sum of the areas ofnsquares inn2. If the areas of the squares can be put in A.P. What is the length of the side of the 25thsquare?a)ab)bc)cd)dCorrect answer is '7'. Can you explain this answer?
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The sum of the areas ofnsquares inn2. If the areas of the squares can be put in A.P. What is the length of the side of the 25thsquare?a)ab)bc)cd)dCorrect answer is '7'. 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 The sum of the areas ofnsquares inn2. If the areas of the squares can be put in A.P. What is the length of the side of the 25thsquare?a)ab)bc)cd)dCorrect answer is '7'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the areas ofnsquares inn2. If the areas of the squares can be put in A.P. What is the length of the side of the 25thsquare?a)ab)bc)cd)dCorrect answer is '7'. Can you explain this answer?.
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