in a housing socity , there are 5184 houses .the houses have been constructed in such a wy that the number of houses in a row is equal to to the number of rows of house . if the first house in particular row is alloted number 1 what will be the last house in a row . please answer fast
Answers
Answer:
Let there be a value of x such that the sum of the number of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it
House H
1
,H
2
,H
3
.......H
x−1
,H
x+1
........H
49
House No. 1 2 3 .......... x -1 x + 1..............49
House number will form an A.P whose first term and the common difference is 1
Sum of n terms S=
2
n
[2a+(n−1)×d]
S
x−1
=S
49
−S
x
⇒
2
(x−1)
[2(1)+(x−1−1)1]=
2
49
[2+48]−
2
x
[2(1)+(x−1)1]
⇒
2
x−1
[2+(x−2)]=
2
49
[50]−
2
x
[2+x−1]
⇒
2
x−1
[x]=
2
49
[50]−
2
x
[x+1]
⇒
2
x
[x−1+x+1]=
2
49
[50]
⇒
2
x
[2x]=49×25
⇒x
2
=49×25
⇒x=7×5=35.
Since x is not a fraction hence the value of x satisfying the given condition exists and is equal to 35.
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