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A child was asked to add first few natural numbers, as long as his patience permitted. As he stopped he gave the sum as 575. When the teacher declared the result was wrong, the child discovered that he had missed one number in the sequence during the addition. The number he missed was

Question

A child was asked to add first few natural numbers, as long as his patience permitted. As he stopped he gave the sum as 575. When the teacher declared the result was wrong, the child discovered that he had missed one number in the sequence during the addition. The number he missed was

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Solution

The sum of the first n natural numbers is given by the formula n*(n+1)/2.

Given that the child's sum was 575, we need to find a number n such that n*(n+1)/2 is just above 575.

By trial and error or using a calculator, we find that n=34 because 34*(34+1)/2 = 595 which is just above 575.

So, the child was trying to add up the first 34 natural numbers but missed one.

The number he missed is therefore 595 (the correct sum of numbers 1 to 34) minus 575 (the sum the child calculated) which equals 20.

So, the child missed the number 20.

This problem has been solved

Similar Questions

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