Which expression correctly represents the sum of the first n natural numbers?
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Answer and explanation
Correct answer: \(\frac{n(n+1)}{2}\)
The natural numbers 1, 2, 3, …, n form an arithmetic progression. Thus, \(S_n=\frac{n}{2}[2+(n-1)] = \frac{n(n+1)}{2}\). Option B gives the sum up to \(n-1\). Exam tip: check that the final term is n before applying the formula.
Frequently asked questions
What is the correct answer to this question?
\(\frac{n(n+1)}{2}\)
Why is this the correct answer?
The natural numbers 1, 2, 3, …, n form an arithmetic progression. Thus, \(S_n=\frac{n}{2}[2+(n-1)] = \frac{n(n+1)}{2}\). Option B gives the sum up to \(n-1\). Exam tip: check that the final term is n before applying the formula.
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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