Question

among the natural numbers 1 to 49 , find the number for which the sum of all the preceeding numbers and the sum of all the succeeding numbers are equal.

Answer 1

number =600 required answer

Answer 2

Answer:

35 is the required number between 1 to 49.

Step-by-step explanation:

Given : Among the natural numbers 1 to 49.

To find : The number for which the sum of all the preceeding numbers and the sum of all the succeeding numbers are equal.

Solution :

Let x be the number from 1 to 49 such that sum of its preceding is equal to the sum of numbers succeeding.

Now According to arithmetic progression,

$1+2+3+.....+(x-1)=(x+1)+(x+2)+(x+3)+.....+49$

$\Rightarrow 1+2+3+.....+(x-1)=[1+2+3+.....+49]-(1+2+3+....+x)$

$\Rightarrow \frac{x(x-1)}{2} =\frac{49\times50}{2}- \frac{x(x-1)}{2}$

After solving above equation we get

$2x^2 = 49\times50$

$x^2 = 49\times25$

$x=\sqrt{1225}$

$x=35$

Hence, 35 is the required number between 1 to 49.