CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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.

Open in App
Solution

Here a=1,d=1 and a49=49

As per question,
Sx1=S49Sx............(i)$

Sx=x2[2+(x1)×1]

= x2(x+1)=x2+x2

Similarly,
Sx1=x12[2+(x11)×1]

= x12(2+x2)=(x1)xxx2x2

Similarly,
S49=492[2+48×1]=492×50=1225

After substituting the values of Sx1,S49 and Sx in equation (1), we get

Sx1==S49Sx

x2x2=1225x2+x2

x2x2+x2+x2=1225

x2x+x2x2=1225

x2=1225

x=35

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Applications of Second Degree Equations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon