Question

The mean of 50 consecutive even natural numbers is equal to the mean of 41
consecutive odd natural numbers. The difference of squares of the greatest of those
even numbers and the middle number of those odd numbers is 7595. What is the
difference between the greatest odd and the greatest even of those numbers?​

Answer 1

Answer:

-9

Step-by-step explanation:

average of consecutive numbers is its middle number

so, the average of 50 consecutive even natural number is average of 25th and 26th number.(ie, even₂₅+1)

Also, the average of 41 consecutive odd numbers is its 21st number.(odd₂₁)

Given they are equal. let it be n

even₂₅+1=odd₂₁=n

even₂₅=n-1

The difference of squares of the greatest of those  even numbers and the middle number of those odd numbers is 7595.

greatest of even numbers is 50th term=even₂₅+25*2=n-1+25*2

                                                                 =n+49

difference=(n+49)^2-n^2=7595

solving this, we get n=53

so,difference between the greatest odd and the greatest even of those numbers=n+40-(n+49)=-9

Answer 2

Answer:

-9

Step-by-step explanation:

The average of consecutive numbers is its middle number

So, the average of 50 consecutive even natural numbers is the average of the 25th and 26th numbers.(ie, even₂₅+1)

Also, the average of 41 consecutive odd numbers is its 21st number.(odd₂₁)

Given they are equal. let it be n

even₂₅+1=odd₂₁=n

even₂₅=n-1

The difference between squares of the greatest of those even numbers and the middle number of those odd numbers is 7595.

The greatest of even numbers is 50th term=even₂₅+25*2 =n+49

difference=(n+49)^2-n^2=7595

solving this, we get n=53

so,difference between the greatest odd and the greatest even of those numbers=n+40-(n+49)= -9

#SPJ2