The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers 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.[Hint : Sx – 1 = S49 – Sx]

The houses of a row are numbered consecutively from 1 to 49. Show that

1.	The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers 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.[Hint : Sx – 1 = S49 – Sx]
Answer» let x be the value such that the sum of the numbers of the houses preceding the house number x is equal to the sum of numbers following it ⇒sum of preceding x=sum of following x 1+2+3.....+(x-1)=(x+1)+(x+2).....+49 ⇒(x-1)/2(1+x-1)=(49-x)/2(x+1+49) (x-1)/x=(49-x)(x+50) x^2-x=49x+2540-x^2-50x x^2-x=2540-x^2-x 2x^2=2540 x^2=1125 x=35 therefore value of x=35 please upvote it