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Question

The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses preceding the house numbered X is equal to sum of the numbers of houses following X.

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Solution

Formula,

Sn=n(n+1)2

Given,

Sx1=S49Sx

(x1)((x1)+1)2=49(49+1)2x(x+1)2

x(x1)=49(50)x(x+1)

x2x=2450x2x

2x2=2450

x2=1225

x=35

Therefore number of houses is 35.

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