What is \(\frac{1}{4}\) of the sum of the first (40) natural numbers?
Answer and explanation
Correct answer: 205
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). For \(n=40\), the sum is \(\frac{40\times41}{2}=820\). One-fourth of this is \(\frac{820}{4}=205\), so option B is correct. A value such as 195 results from an error in finding the sum or dividing it. Exam tip: first calculate the total using \(\frac{n(n+1)}{2}\), then take the required fraction.
Frequently asked questions
What is the correct answer to this question?
205
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). For \(n=40\), the sum is \(\frac{40\times41}{2}=820\). One-fourth of this is \(\frac{820}{4}=205\), so option B is correct. A value such as 195 results from an error in finding the sum or dividing it. Exam tip: first calculate the total using \(\frac{n(n+1)}{2}\), then take the required fraction.
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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