Question

PLEASE ANSWER IT FAST.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

35

Step-by-step explanation:

The number of houses preceding x is x - 1.

It can be observed that Sum of the number of houses preceding the house numbered,x = 1 + 2 + 3 + ... + x - 1.

These numbers form an AP with a = 1, d = 1, n = 49.

∴ Sum of n terms of an AP sn = (n/2)[2a + (n - 1) * d]

Now,

Sₓ₋₁ = S₄₉ - Sₓ

$=>\frac{x-1}{2}[2a+(x-1-1)d) =\frac{49}{2}(2a+48d) -\frac{x}{2}(2a+(x-1) d)$

$=>\frac{x-1}{2}[2 * 1+(x-2)*1)=\frac{49}{2}[2 * 1 + 48 * 1] - \frac{x}{2}[2 * 1 + (x - 1)*1]$

$=>(x-1)(2+x-2)=49(2+48) - x(2 + x - 1)$

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

$=>x^2 - x =2450-x-x^2$

$=>2x^2 = 2450$

$=>x^2 = 1225$

$=> x=35,-35$

However the house numbers are positive only, The value of x will be 35.

Therefore, the value of x is 35.

Hope it helps!