Question
The houses of a row are numbered consecutively from 1 to 49. Show that 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.
Solution
The consecutive numbers on the houses of a row are 1, 2, 3, ... 49.
Clearly this list of number forming an A .P.
Here, a = 1,d = 2 – 1 = 1
According to the question,
Hence the required values of x is 35.
