If the mean of first n natural numbers is 5n/9, then n =?
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Answered by
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Given that the mean of first n natural numbers = 5n/9.
We know that mean of n natural numbers = (n + 1)/2.
(n + 1)/ 2 = 5n/9
9(n + 1) = 2(5n)
9n + 9 = 10n
9 = n.
Therefore the value of n = 9.
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Answered by
2
Given:
The mean of the first n natural numbers is (5n/9).
To Find:
The value of n is?
Solution:
1. The mean of the first n natural number is (5n/9).
2. Let 1, 2, 3, ..., n be n consecutive natural numbers.
=> The sum of the first n natural numbers ( Consecutive ) is given by the formula = (n)(n+1)/2.
3. Let X1, X2, X3, X4, ..., Xn be n terms. The average of the n terms if given by the formula,
=> Average = (X1 + X2 + X3 +... Xn)/n.
=> Average = ( 1 + 2 + 3 + .. + n) /n,
=> (5n/9) = [(n)(n+1)]/(2n), ( Solve for value of n )
=> (5/9) = (n+1)/2n,
=> (10n)/9 = n + 1,
=> 10n = 9n + 9,
=> 10n - 9n = 9,
=> n = 9.
Therefore, the value of n is 9.
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