Question

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

Answer 1

given 1,2,3,4,5,....49 consecutive numbersx is the number such that sum of preceding numbers of x = sum of following numbers of xsum 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-x²-50xx²-x =2450-x²-xx²+x²-x+x=24502x²=2450x²=2450/2x²=1225x=√1225x=35required number is x= 35sum of (1,2,3.....34) = sum of (36,37,....49)
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Answer 2

Hey! Your answer is in the following attachment.