Question

if the mean of the first 'N' natural number is 5x/9. find x​

Answer 1

value of x = 9(N + 1)/10

it is given that,

The mean of the first N natural numbers is 5x/9.

first find sum of N natural numbers.

1 + 2 + 3 + 4 + ... + N = N/2 [2 × 1 + (N - 1) × 1]

= N(N + 1)/2

so, sum of N natural numbers is N(N + 1)/2

now mean = sum of observations/total number of observations

= {N(N + 1)/2}/N

= (N + 1)/2

so, mean of N natural numbers is (N + 1)/2

⇒(N + 1)/2 = 5x/9

⇒(N + 1) = 10x/9

⇒x = 9(N + 1)/10

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