What is the ratio of (S_{20}) to (S_{10})?
Answer and explanation
Correct answer: \(42:11\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{20}=\frac{20\times21}{2}=210\) and \(S_{10}=\frac{10\times11}{2}=55\). Hence, \(S_{20}:S_{10}=210:55=42:11\). The ratio \(21:5\) would result from incorrectly taking \(S_{10}\) as 50. 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?
\(42:11\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{20}=\frac{20\times21}{2}=210\) and \(S_{10}=\frac{10\times11}{2}=55\). Hence, \(S_{20}:S_{10}=210:55=42:11\). The ratio \(21:5\) would result from incorrectly taking \(S_{10}\) as 50. 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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