What is the sum of (1+2+3+\cdots+75)?
Answer and explanation
Correct answer: 2850
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Here, \(n=75\), so \(\frac{75\times 76}{2}=75\times 38=2850\). Therefore, 2850 is correct. A value such as 2825 does not result from multiplying 75 by its next number, 76, as required by the formula. Exam tip: For the sum from \(1\) to \(n\), directly use \(\frac{n(n+1)}{2}\).
Frequently asked questions
What is the correct answer to this question?
2850
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Here, \(n=75\), so \(\frac{75\times 76}{2}=75\times 38=2850\). Therefore, 2850 is correct. A value such as 2825 does not result from multiplying 75 by its next number, 76, as required by the formula. Exam tip: For the sum from \(1\) to \(n\), directly use \(\frac{n(n+1)}{2}\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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