What is the ratio of (S_{30}) to (S_{15})?
Answer and explanation
Correct answer: \(31:8\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{30}=\frac{30\times31}{2}=465\) and \(S_{15}=\frac{15\times16}{2}=120\). Therefore, \(S_{30}:S_{15}=465:120=31:8\). The ratio \(31:9\) would result from using an incorrect value for the second sum. Exam tip: simplify a ratio at the end by dividing both terms by their greatest common factor.
Frequently asked questions
What is the correct answer to this question?
\(31:8\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{30}=\frac{30\times31}{2}=465\) and \(S_{15}=\frac{15\times16}{2}=120\). Therefore, \(S_{30}:S_{15}=465:120=31:8\). The ratio \(31:9\) would result from using an incorrect value for the second sum. Exam tip: simplify a ratio at the end by dividing both terms by their greatest common factor.
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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