Question

as a punishment, teacher told rohan to write sum of first 1 natural number, sum of first 2 natural numbers, sum of first 3 natural numbers and so on, on blackboard. at one instance, rohan wrote 600. the teacher stopped him and said that it is wrong, as sum of first n natural numbers can never be 600. rohan discovered that he has missed one number during addition. can you identify the missing number for us.

Answer 1

The missing number is 135

Let's assume Rohan was supposed to write the sum of the first n natural numbers, where n is a positive integer. Since the sum cannot be 600, this means he made a mistake in the addition.

Let x be the missing number. Then, the sum of the first n natural numbers without the missing number is 600 - x.

We know that the sum of the first n natural numbers is given by the formula:

n(n+1)/2

Therefore, we can set up the following equation:

n(n+1)/2 = 600 - x

Multiplying both sides of the equation by 2, we get:

n(n+1) = 1200 - 2x

To find the missing number x, we need to find the values of n and simplify the equation.

We can try different values of n until we find a value that satisfies the equation. For example, if n = 30, then the equation becomes:

30(30+1) = 1200 - 2x

930 = 1200 - 2x

2x = 270

x = 135

Therefore, the missing number is 135.