If (S_n=12246), what is the value of (n)?
Answer and explanation
Correct answer: 156
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Therefore, \(\frac{n(n+1)}{2}=12246\). On substituting \(n=156\), we get \(\frac{156\times157}{2}=78\times157=12246\). Hence, 156 is correct. For the closest distractor, \(n=155\) gives \(\frac{155\times156}{2}=12090\), not 12246. Exam tip: when answer choices are given, substituting them in the formula is often the quickest reliable check.
Frequently asked questions
What is the correct answer to this question?
156
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Therefore, \(\frac{n(n+1)}{2}=12246\). On substituting \(n=156\), we get \(\frac{156\times157}{2}=78\times157=12246\). Hence, 156 is correct. For the closest distractor, \(n=155\) gives \(\frac{155\times156}{2}=12090\), not 12246. Exam tip: when answer choices are given, substituting them in the formula is often the quickest reliable check.
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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