Question

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.

Answer 1

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Answer 2

ɢɪᴠᴇɴ 1,2,3,4,5,....49 ᴄᴏɴsᴇᴄᴜᴛɪᴠᴇ ɴᴜᴍʙᴇʀs

x ɪs ᴛʜᴇ ɴᴜᴍʙᴇʀ sᴜᴄʜ ᴛʜᴀᴛ

sᴜᴍ ᴏғ ᴘʀᴇᴄᴇᴅɪɴɢ ɴᴜᴍʙᴇʀs ᴏғ x = sᴜᴍ ᴏғ ғᴏʟʟᴏᴡɪɴɢ ɴᴜᴍʙᴇʀs ᴏғ x

sᴜᴍ ᴏғ ( 1,2,3,....x-1) = sᴜᴍ ᴏғ [(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

ʀᴇϙᴜɪʀᴇᴅ ɴᴜᴍʙᴇʀ ɪs x= 35

sᴜᴍ ᴏғ (1,2,3.....34) = sᴜᴍ ᴏғ (36,37,....49)