What is twice the sum of the first (54) natural numbers?
Answer and explanation
Correct answer: 2970
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Therefore, \(S_{54}=\frac{54\times55}{2}=1485\). Twice this sum is \(2\times1485=2970\). \(2916\) is \(54^2\), so it is not twice the required sum. Exam tip: when the question asks for twice the sum, the 2 cancels in \(\frac{n(n+1)}{2}\), giving \(n(n+1)\).
Frequently asked questions
What is the correct answer to this question?
2970
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Therefore, \(S_{54}=\frac{54\times55}{2}=1485\). Twice this sum is \(2\times1485=2970\). \(2916\) is \(54^2\), so it is not twice the required sum. Exam tip: when the question asks for twice the sum, the 2 cancels in \(\frac{n(n+1)}{2}\), giving \(n(n+1)\).
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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