Question

the mean of first n natural numbers is x. what is the mean of first n even natural numbers ​

Answer 1

2X
mean of first n natural numbers, X = (1+2+3+......+n)/n
mean of first n even natural numbers = (2+4+6+....+2n)/n = 2(1+2+3+...+n)/n=2X

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Answer 2

Answer:

Mean of first n even Natural No. is 2x.

Step-by-step explanation:

Given: Mean of first n natural numbers = x

To find: Mean of first n even natural number

First n natural numbers are 1 , 2 , 3 , 4 , 5 , 6 , ... , n

Mean of first n natural numbers = x

$mean=\frac{sun\:of\:all\:observation}{Total\:no.\:of\:observation}$

$\implies\frac{1+2+3+4+5+6+...+n}{n}=x$ ............(1)

First n even natural nos are 2 , 4 , 6 , 8 , 10 , ... , 2n

Mean of first n even natural no = $\frac{2+4+6+8+10+...+2n}{n}$

                                                   = $\frac{2(1+2+3+4+5+...+n)}{n}$

                                                   = $2\times\frac{1+2+3+4+5+...+n}{n}$

                                                   = $2\times x$      ( from (1) )

Therefore, Mean of first n even Natural No. is 2x.