Question

If the mean of first n natural numbers is `(5n)/9,` then n =?

Options

• 6

• 7

• 9

• 10

Answer 1

9

Explanation:-

Since natural numbers forms an A.P,

∴ Sum of n natural numbers is:

`S_n=n/2[2a+(n-1)d]`

`S_n=n/2[2xx1+(n-1)1]`

`S_n=n/2[n+1]`

But according to question,

`barx=(n/2[n+1])/n=(5n)/9`

`=>1/2[n+1]=(5n)/9`

⇒ 9n + 9 = 10n

⇒ n = 9