The houses of a row are number consecutively from 1 to 49. Show that there is a value of x such that the sum of numbers of the houses preceding the house numbered x is equal to the sum of the number of houses following it.
Find this value of x.
[Hint Sx − 1 = S49 − Sx]
The number of houses was
1, 2, 3 … 49
It can be observed that the number of houses are in an A.P. having a as 1 and d also as 1.
Let us assume that the number of xth house was like this.
We know ...
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