Houses in a row are numbered from 1 to 49

Asked by admin @ 03/08/2021 in Math viewed by 269 People

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 houses preceding the house numbered x is equal to the sum of the numbers of the houses following it . Find this value of x.

Answered by admin @ 03/08/2021

Given 1,2,3,4,5,....49 consecutive numbers
x is the number such that
sum of preceding numbers of x = sum of following numbers of x
sum of ( 1,2,3,....x-1) = sum of [(x+1), (x+2) ,....48,49]

(x-1)/2[1+x-1] =(49-x)/2[x+1+49]
(x-1)x=(49-x)(x+50)
x²-x=49x+2450-x²-50x
x²-x =2450-x²-x
x²+x²-x+x=2450
2x²=2450
x²=2450/2
x²=1225
x=√1225
x=35
required number is x= 35
sum of (1,2,3.....34) = sum of (36,37,....49)

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