Question

If the mean of first n natural numbers is \[\frac{5n}{9}\], then n =

Options

• 5

• 4

• 9

• 10

Answer 1

Given:
Mean of first n natural number = \[\frac{5n}{9}\]

\[\Rightarrow \frac{1 + 2 + 3 + . . . + n}{n} = \frac{5n}{9}\]

\[ \Rightarrow \frac{\frac{n\left( n + 1 \right)}{2}}{n} = \frac{5n}{9}\]

\[ \Rightarrow \frac{n + 1}{2} = \frac{5n}{9}\]

\[ \Rightarrow 9n + 9 = 10n\]

\[ \Rightarrow n = 9\]