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


Show that there is a valueof x such that the sum of the numbers of the houses preceding the house numbered x isequal to the sum of the numbers of the houses following it. Find this value of x

Best Answer

Solution:In this question: a = 1, d = 1 and a49 = 49

According to question:

S(x-1) = S49 - Sx       (i)

The sum of x terms can be calculated as:

were

= 1225

Now,

After using the values of Sx-1, S49 and Sx in (i), we get;

Sx-1 = S49  -Sx

(x2 –x)/2 = 1225 - (x2 –x)/2

(x2 –x +x2+x)/2

(2x2)/2

x2 = 1225

x = 35

 

Talk to Our counsellor