The house of a row are …

The consecutive numbers on the houses of a row are 1, 2, 3, ..., 49
Clearly this list of number forming an AP.
Here, a = 1
d = 2 - 1 = 1
S_x-1 = S₄₉ - Sx
{tex} \Rightarrow \frac{{x - 1}}{2}[2a + (x - 1 - 1)d] - \frac{x}{2}[2a + (x - 1)d]{/tex}
{tex}\because {S_n} = \frac{n}{2}[2a + (n - 1)d]{/tex}
{tex} \Rightarrow \frac{{x - 1}}{2}[2(1) + (x - 2)(1)]{/tex} {tex} = \frac{{49}}{2}[2(1) + (48)(1)] - \frac{x}{2}[2(1) + (x - 1)(1)]{/tex}
{tex} \Rightarrow \frac{{x - 1}}{2}[x] = 1225 - \frac{{x(x + 1)}}{2}{/tex}
{tex} \Rightarrow \frac{{(x - 1)(x)}}{2} + \frac{{x(x + 1)}}{2} = 1225{/tex}
{tex} \Rightarrow \frac{x}{2}(x - 1 + x + 1) = 1225{/tex}
{tex} \Rightarrow {x^2} = 1225{/tex}
{tex} \Rightarrow x = \sqrt {1225} {/tex}
{tex} \Rightarrow x = 35{/tex}
Hence, the required value of x is 35.