Question

If the mean of n natural numbers is 5n/9 then n?

Answer 1

Hi there!

We know that,
Mean of first n Natural numbers is n+1/2

ATQ,

5n/9 = n+1/2

10n = 9n + 1

10n - 9n = 1

n = 1

Hence,
No. of terms is 1

Cheers!

Answer 2

Answer:

The value of n is 9.

Step-by-step explanation:

The natural numbers are

1, 2, 3, ....

The sum of n natural number is

$S_n=\frac{n(n+1)}{2}$

The mean of n natural numbers is

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

It is given that the mean of n natural numbers is 5n/9.

$\frac{(n+1)}{2}=\frac{5n}{9}$

$9(n+1)=2(5n)$

$9n+9=10n$

$9=10n-9n$

$9=n$

Therefore the value of n is 9.