Question

The mean of 30 consecutive natural
numbers is x and the mean of the odd
numbers in these 30 natural numbers is y.
If the smallest number is an odd number,
find the value of x - y.​

Answer 1

Answer:

x-y= 1/2

.

Explanation:

Given : The mean of 30 consecutive natural numbers is x and the mean of the odd numbers in these 30 natural numbers is y.

The smallest number is an odd number,

To find : the value of x - y.

Solution:

The smallest number is an odd number,

Assume 30 natural numbers are

2k+1 , 2k + 2 , ... , 2k + 29 , 2k + 30

15 odd natural numbers in these are

2k + 1 , 2k + 3 , .... , 2k + 29

where k is non negative integer

Sₙ = (n/2) (first term + nth Term)

Mean = ( first Term + nth term)/2

Mean of 30 natural numbers

x= (2k +1 + 2k + 30)/2

x = 2k + 15.5

Mean of 15 odd natural numbers

y= (2k +1 + 2k + 29)/2

y = 2k + 15

x - y = 2k + 15.5 - (2k + 15)

=> x - y = 0.5

the value of x - y is 0.5