Which of the following sets represents numbers obtained as the sum of the first n natural numbers (triangular numbers)?
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Answer and explanation
Correct answer: \(\left\{\frac{n(n+1)}{2}:n\in\mathbb{N},\ n\geq1\right\}\)
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\), so option A gives the set of triangular numbers. For example, \(n=3\) gives 6. Squares form a different set. In exams, identify the standard sum formula before choosing.
Frequently asked questions
What is the correct answer to this question?
\(\left\{\frac{n(n+1)}{2}:n\in\mathbb{N},\ n\geq1\right\}\)
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\), so option A gives the set of triangular numbers. For example, \(n=3\) gives 6. Squares form a different set. In exams, identify the standard sum formula before choosing.
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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