Question

The houses of a street are numbered from 1 to 49. Senthil's house is numbered such that the
sum of numbers of the houses prior to Senthil's house is equal to the sum of numbers of the
houses following Senthil's house. Find Senthil's house number.​

Answer 1

Answer:

SENTHIL'S HOUSE NUMBER IS 25

Answer 2

Senthil's house number would be 35.

Step-by-step explanation:

Let the number of Senthil's house = x

Since the sum of numbers of the houses prior to Senthil's house = the sum of numbers of the houses following Senthil's house.

The house no. preceding x = x-1

The sum of house no. preceding x = $S_{x-1}$

The sum of house no. following x = $S_{49}-S_{x}$

Therefore,   $S_{x-1}=S_{49} - S_{x}$

Now using the sum of n term formula, the equation would be :

$\frac{(x-1(1+x-1)}{2}=\frac{(49-x)(x+1+49)}{2}$

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

x²-x = 49x - x² + 49 × 50 - 50x

x² - x + x + x² = 49 × 50

2x² = 49 × 50

x² = 49 × 25

x² = 7² × 5²

x = 7 × 5

x = 35

Senthil's house number would be 35.

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