Question

Example 2.38

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 ?

Solution :

Let Senthil's house number be x.

It is given that 1 + 2 + 3 + .... + (x – 1)

= (x – 1) + (x + 2) + .... + 49

1 + 2 + 3 + ...... + (x – 1)

= [1 + 2 + 3 + .... + 49] – [1 + 2 + 3 +.... + x]

2 22

2

1 2 3 ... ( 1)

[1 2 3 ... 49] [1 2 3 ... ]

1 49 [1 ( 1)] [1 49] [1 ] 2 22

( 1) 49 50 ( 1)

222

2450 2 2450

1225 gives 35

x

x

x x

x x

x x x x

xx xx x

x x

+++ + −

= +++ + − +++ +

− +−= + − +

−× + = −

−= − −⇒ =

= =

Therefore, Senthil's hosue number is 35.​

Answer 1

Answer:

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