The houses of 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 the value of x ?

1) 22
2) 19
3) 28
4) 35

• 35
  
  If y=x-1, then
  Sum of first y terms= y*(y+1)/2
  sum of all 49 terms = 49*50/2=1225
  
  as per condition,
  2*y*(y+1)/2 +(y+1)= 1225
  (y+1)^2=35^2
  y+1=x=35
• 11 years agoHelpfull: Yes(1) No(1)