Question

The mean of first n natural numbers is x what is the mean of first n even natural numbers

Answer 1

Answer:

2x

Step-by-step explanation:

Mean of first n natural numbers= x (Given)

Let y be sum of first n natural numbers and z be the sum of first n even natural numbers. Thus mean =

Mean of first n natural numbers = y / n (1)

Mean of first n even numbers = z / n  (2)

On multiplying each natural number from given first n natural numbers by 2 we will get the first n even numbers. Therefore

Sum of first n even natural numbers= 2×(sum of first n natural number )

Sum of first n even natural numbers=2×(y) = 2y

Thus, z = 2y (3)

Substituting (3) in equation (2)-

Mean of first n even numbers = 2y / n=2(y/n)

Mean of first  n even numbers =2(mean of first n natural numbers)

Since mean of first n natural  numbers  = x

Thus the mean of first n even  numbers  =2(x)=2x