. 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:
= 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
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