Question

please answer me fast class 10​

Answer 1

=> Let us assume that the required house no. is x.

Sum of the numbers of houses preceding x is equal to sum of the numbers of houses following it.

Sum of first n natural numbers is given by n*(n+1)/2.

So,Sum of numbers of houses preceeding x is sum of first x-1 numbers = (x-1)*x/2.

Now, Sum of numbers of houses following it is equal to sum of first n houses minus sum of first x houses:

= n*(n+1)/2 - x*(x+1)/2.

A/Q, They both are equal.

So, We have

(x-1)*x/2 = n*(n+1)/2 - x*(x+1)/2

=> (x-1)*x/2+(x+1)*x/2 = n*(n+1)/2

=>x*(x-1+x+1)/2 = n*(n+1)/2

=>x*2x/2 = n*(n+1)/2

Putting n=49, we get

=>x²=49*50/2

=>x²=49*25

=>x²=7²*5²

=>x= √(49*25) = √1225

Therefore, x=35

Hence 35 is the number of the house such that Sum of the numbers of houses preceding it is equal to sum of the numbers of houses following it.

Hope that helps. :)

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