Question

the houses in a row are numbered consequently from 1 to 49 show that there exists a value of that it's such that sum of numbers of house preceding the house number x is equal to sum of the numbers of housing following x

Answer 1

Answer:

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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