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If \(S_n=\frac{n(n+1)}{2}\), what is the value of \(S_{2n}\) when \(n=15\)?
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Answer and explanation
Correct answer: 465
For \(n=15\), the index \(2n\) becomes 30. Hence, \(S_{2n}=S_{30}=\frac{30(30+1)}{2}=\frac{30\times31}{2}=465\). Option 435 equals \(S_{29}\), so it is not correct. Exam tip: evaluate the index \(2n\) before substituting into the formula.
Frequently asked questions
What is the correct answer to this question?
465
Why is this the correct answer?
For \(n=15\), the index \(2n\) becomes 30. Hence, \(S_{2n}=S_{30}=\frac{30(30+1)}{2}=\frac{30\times31}{2}=465\). Option 435 equals \(S_{29}\), so it is not correct. Exam tip: evaluate the index \(2n\) before substituting into 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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