# The houses of a row are there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.

Therefore, sum of house numbers preceding x = Sx-1

And sum of house numbers following x = S49 – Sx

Given,

Sx-1 = S49 – Sx

(x – 1)/2[2a + x(x – 1 – 1)d] = 49/2[2a + (49 – 1)d] – x/2[2a + (x – 1)d]

On solving, we get,

(x + 35)(x – 35) = 0

Therefore, x = -35 or x = 35

Number of houses cannot be negative

Therefore, x = 35