Question:
A child was asked to add first few natural numbers (i.e. \( 1 + 2 + 3 + \dots \)) so long his patience permitted. As he stopped, he gave the sum as 575. When the teacher declared the result wrong, the child discovered he had missed one number in the sequence during addition. The number he missed was:
A child was asked to add first few natural numbers (i.e. \( 1 + 2 + 3 + \dots \)) so long his patience permitted. As he stopped, he gave the sum as 575. When the teacher declared the result wrong, the child discovered he had missed one number in the sequence during addition. The number he missed was:
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Use the formula for the sum of the first \( n \) natural numbers to identify the missing number.
Updated On: Aug 4, 2025
- less than 10
- 10
- 15
- more than 15
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The Correct Option is C
Solution and Explanation
The sum of the first \( n \) natural numbers is given by:
\[
S = \frac{n(n + 1)}{2}.
\]
The closest sum to 575 is:
\[
\frac{34 \times 35}{2} = 595.
\]
The child missed 595 - 575 = 20, and the missing number is 15. Thus, the Correct Answer is 15.
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