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A function f(x) satisfies f(1) = 3600, and f(1) + f(2) +...+ f(n) = n² f(n), for all positive integers n > 1. What is the value of f(9) ?
- a)80
- b)240
- c)200
- d)100
- e)120
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A function f(x) satisfies f(1) = 3600,and f(1) + f(2) +...+ f(n) = n&s...
f(1) = 3600 , f(1) + f(2) = 4 * f(2).
f(2) = f(1)/3. We can write this as f(2) = f(1) * 1/3.
Now, f(1) + f(2) + f(3) = 9 * f(3).
f(3) = f(1) + f(2) / 8. We know f(2) = f(1) / 3.
So, f(3) = f(1) + (f(1)/3) / 8.
We can write this as f(3) = f(1) *1/3 * 2/4. Since we already have f(1) * 1/3, we write it in such a way that the equation has f(1) * 1/3 and then what comes rest, so that we can generalize
Calculating similarly for f(4), we get f(4) = f(1) * 1/3 * 2/4 * 3/5.
So, f(9) will be f(1) * 1/3 * 2/4 * 3/5 * 4/6 * 5/7 *6/8 * 7/9 * 8/10.
=> f(9) = (f(1) * 1 * 2) / (9 *10).
=> f(9) = 3600 * 2/ 9 * 10 = 80.
Calculating similarly for f(4), we get f(4) = f(1) * 1/3 * 2/4 * 3/5.
So, f(9) will be f(1) * 1/3 * 2/4 * 3/5 * 4/6 * 5/7 *6/8 * 7/9 * 8/10.
=> f(9) = (f(1) * 1 * 2) / (9 *10).
=> f(9) = 3600 * 2/ 9 * 10 = 80.
Most Upvoted Answer
A function f(x) satisfies f(1) = 3600,and f(1) + f(2) +...+ f(n) = n&s...
We cannot determine the value of f(2) or any other value of f(x) with the given information. The equation f(1) + f(2) + ... + f(n) = n does not provide any specific relationship between the values of f(x) for different values of x. Therefore, we need more information about the function to determine its values for specific inputs.
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Community Answer
A function f(x) satisfies f(1) = 3600,and f(1) + f(2) +...+ f(n) = n&s...
f(1) = 3600 , f(1) + f(2) = 4 * f(2).
f(2) = f(1)/3. We can write this as f(2) = f(1) * 1/3.
Now, f(1) + f(2) + f(3) = 9 * f(3).
f(3) = f(1) + f(2) / 8. We know f(2) = f(1) / 3.
So, f(3) = f(1) + (f(1)/3) / 8.
We can write this as f(3) = f(1) *1/3 * 2/4. Since we already have f(1) * 1/3, we write it in such a way that the equation has f(1) * 1/3 and then what comes rest, so that we can generalize
Calculating similarly for f(4), we get f(4) = f(1) * 1/3 * 2/4 * 3/5.
So, f(9) will be f(1) * 1/3 * 2/4 * 3/5 * 4/6 * 5/7 *6/8 * 7/9 * 8/10.
=> f(9) = (f(1) * 1 * 2) / (9 *10).
=> f(9) = 3600 * 2/ 9 * 10 = 80.
Calculating similarly for f(4), we get f(4) = f(1) * 1/3 * 2/4 * 3/5.
So, f(9) will be f(1) * 1/3 * 2/4 * 3/5 * 4/6 * 5/7 *6/8 * 7/9 * 8/10.
=> f(9) = (f(1) * 1 * 2) / (9 *10).
=> f(9) = 3600 * 2/ 9 * 10 = 80.
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A function f(x) satisfies f(1) = 3600,and f(1) + f(2) +...+ f(n) = n² f(n),for all positive integers n > 1. What is the value of f(9) ?a)80b)240c)200d)100e)120Correct answer is option 'A'. Can you explain this answer?
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A function f(x) satisfies f(1) = 3600,and f(1) + f(2) +...+ f(n) = n² f(n),for all positive integers n > 1. What is the value of f(9) ?a)80b)240c)200d)100e)120Correct answer is option 'A'. 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 A function f(x) satisfies f(1) = 3600,and f(1) + f(2) +...+ f(n) = n² f(n),for all positive integers n > 1. What is the value of f(9) ?a)80b)240c)200d)100e)120Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function f(x) satisfies f(1) = 3600,and f(1) + f(2) +...+ f(n) = n² f(n),for all positive integers n > 1. What is the value of f(9) ?a)80b)240c)200d)100e)120Correct answer is option 'A'. Can you explain this answer?.
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