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.

Question

Philoid · Accepted Answer

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

According to question:

S_(x-1) = S₄₉ - S_x (i)

The sum of x terms can be calculated as:

S_x

= (x²+x)/2

Now, sum of 49 :

S_x

= 1225

Now,

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

S_{x-1 =} S₄₉ -S_x

(x² –x)/2 = 1225 - (x² –x)/2

(x² –x +x²+x)/2

(2x²)/2

x² = 1225

x = 35

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.[Hint :]

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.
[Hint :]