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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 575. The teacher stopped him and said that it is wrong, as sum of first n natural numbers can never be 575. Rohan discovered that he has missed one number during addition. Can you identify the missing number for us.00 : 18 : 1911/15 attemptedEndOptions: Pick one correct answer from below1015More than 15Less than 10

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 575. The teacher stopped him and said that it is wrong, as sum of first n natural numbers can never be 575. Rohan discovered that he has missed one number during addition. Can you identify the missing number for us.00 : 18 : 1911/15 attemptedEndOptions: Pick one correct answer from below1015More than 15Less than 10

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Solution

The sum of the first n natural numbers is given by the formula n*(n+1)/2. If Rohan wrote 575, we need to find a natural number n such that n*(n+1)/2 is close to 575 but less than 575.

Let's try with n=34, we get 34*(34+1)/2 = 595 which is more than 575. So, n is less than 34.

Let's try with n=33, we get 33*(33+1)/2 = 561 which is less than 575.

So, the sum of first 33 natural numbers is 561. The difference between 575 and 561 is 14.

Therefore, Rohan missed the number 14 while adding.

So, the correct answer is "More than 15".

This problem has been solved

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