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If \(S_n=\frac{n(n+1)}{2}\) and \(S_n=861\), what is the value of (n)?
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Answer and explanation
Correct answer: 41
Given \(\frac{n(n+1)}{2}=861\), we get \(n(n+1)=1722\). Since \(41\times42=1722\), \(n=41\). For the close distractor \(40\), the sum is \(\frac{40\times41}{2}=820\), not 861. Exam tip: look for two consecutive numbers whose product equals twice the given sum.
Frequently asked questions
What is the correct answer to this question?
41
Why is this the correct answer?
Given \(\frac{n(n+1)}{2}=861\), we get \(n(n+1)=1722\). Since \(41\times42=1722\), \(n=41\). For the close distractor \(40\), the sum is \(\frac{40\times41}{2}=820\), not 861. Exam tip: look for two consecutive numbers whose product equals twice the given sum.
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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