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If the mean of first n natural number is 15, what is the value of n?
- a)29
- b)30
- c)15
- d)14
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the mean of first n natural number is 15, what is the value of n?a)...
Understanding the Problem
To find the number of natural numbers (n) such that their mean equals 15, we first need to understand how to calculate the mean of the first n natural numbers.
Mean of Natural Numbers
The mean (average) of the first n natural numbers is given by the formula:
Mean = (Sum of first n natural numbers) / n
The sum of the first n natural numbers can be calculated using the formula:
Sum = n(n + 1) / 2
So, we can express the mean as:
Mean = (n(n + 1) / 2) / n = (n + 1) / 2
Setting Up the Equation
According to the problem, the mean is given as 15. Thus, we can set up the equation:
(n + 1) / 2 = 15
To eliminate the fraction, multiply both sides by 2:
n + 1 = 30
Solving for n
Now, subtract 1 from both sides to find n:
n = 30 - 1
n = 29
Conclusion
Thus, the value of n is 29, which corresponds to option 'A'.
- The mean of the first 29 natural numbers equals 15.
- Therefore, the correct answer is option 'A'.
To find the number of natural numbers (n) such that their mean equals 15, we first need to understand how to calculate the mean of the first n natural numbers.
Mean of Natural Numbers
The mean (average) of the first n natural numbers is given by the formula:
Mean = (Sum of first n natural numbers) / n
The sum of the first n natural numbers can be calculated using the formula:
Sum = n(n + 1) / 2
So, we can express the mean as:
Mean = (n(n + 1) / 2) / n = (n + 1) / 2
Setting Up the Equation
According to the problem, the mean is given as 15. Thus, we can set up the equation:
(n + 1) / 2 = 15
To eliminate the fraction, multiply both sides by 2:
n + 1 = 30
Solving for n
Now, subtract 1 from both sides to find n:
n = 30 - 1
n = 29
Conclusion
Thus, the value of n is 29, which corresponds to option 'A'.
- The mean of the first 29 natural numbers equals 15.
- Therefore, the correct answer is option 'A'.
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If the mean of first n natural number is 15, what is the value of n?a)29b)30c)15d)14Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the mean of first n natural number is 15, what is the value of n?a)29b)30c)15d)14Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean of first n natural number is 15, what is the value of n?a)29b)30c)15d)14Correct answer is option 'A'. Can you explain this answer?.
If the mean of first n natural number is 15, what is the value of n?a)29b)30c)15d)14Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the mean of first n natural number is 15, what is the value of n?a)29b)30c)15d)14Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mean of first n natural number is 15, what is the value of n?a)29b)30c)15d)14Correct answer is option 'A'. Can you explain this answer?.
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