Question

The houses of a row are numbered consecutively from 1 to 49. Show that there is 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 houses following it. Find the value of x.

Answer 1

Consecutively marked number of houses are 1, 2, 3, 4 …… 47, 48, 49.

x is such number so that sum of one side of x numbers = sum of other side number of x d in all the terms of series = 1.

then sum of number from 1 to x – 1, (a) = 12, n = x – 1.

and sum of numbers from x + 1 to 49

Then according to question,

Hence, value of x is 35.