Question

if the mean of first n natural numbers is 5 x upon 9 then x is equal to​

Answer 1

The value of x is $\frac{9(n+1)}{10}$

Step-by-step explanation:

Mean of first n natural numbers = $\frac{5x}{9}$

Sum of first n natural numbers = $\frac{n(n+1)}{2}$

Mean is the average of first n natural numbers.

Mean = $\frac{[\frac{n(n+1)}{2} ]}{n}$= $\frac{n(n+1)}{2n} = \frac{n+1}{2}$

Mean of first n natural numbers = $\frac{5x}{9}$

=> $\frac{n+1}{2} = \frac{5x}{9}$

=> 2(5x) = 9(n+1)

=> 10x = 9(n+1)

=> x = $\frac{9(n+1)}{10}$

Hence, the value of x is $\frac{9(n+1)}{10}$