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 numbers of the houses preceding the houses number x is equal to the sum of numbers of houses following it find the value of x.

Answer 1

I hope you will get the my answer

Answer 2

Answer:

The total number of houses preceding the house numbered x = (x-1)

and the number of housed following the house numbered x = 49-x

The house number following the house number x = x+1

According to quesiton

Sx-1 = S4 9-x

For the house preceding house number x:a = 1, d = 1, n = x-1

For the house following house number x:a = x+1, d = 1, last term, l = 49

So,

[(x-1)/2][2(1)+(x-1-1)(1)} = [(49-x)/2][(x+1)+49]

[(x-1)/2]92+x-2) = [(49-x)/2](50+x)

(x-1)(x) = (49-x)(50+x)

x2 - x = 2450 + 49x - 50x - x2

x2 - x = 2450 - x - x2

x2 - x + x + x2 = 2450

2x2 = 2450

x2 = 2450/2 = 1225

x = sqrt(1225)

x = 35