Question

If the mean of first n natural numbers is 5n/9, then n =
(a)5
(b)4
(c)9
(d)10

Answer 1

SOLUTION :  

The correct option is (c) : 9

Given : MEAN of first n natural number = 5n/9

First n natural numbers are : 1,2,3,.........n

MEAN = Sum of all the observations/ Total number of observations

5n/9 = (1 + 2 +3 + ……+ n)/n

5n/9 = n(n +1)/2 / n  

[The sum of the first n natural numbers : n(n +1)/2]

5n/9 = (n +1)/2  

5n × 2 = 9(n + 1)  

10n = 9n + 9

10n - 9n = 9  

n = 9  

Hence, the value of n is 9.

HOPE THIS ANSWER WILL HELP YOU……

Answer 2

mean of first n natural numbers

= ( n + 1 )/2--( 1 )

according to the problem given ,

mean of first n natural numbers = 5n/9 ---( 2 )

Therefore ,

( 1 ) = ( 2 )

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

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

9( n + 1 ) = 5n × 2

9n + 9 = 10n

9 = 10n - 9n

9 = n

n = 9

So, the correct option is (c) 9