What is the ratio of (S_{60}) to (S_{30})?
Answer and explanation
Correct answer: \(122:31\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{60}=\frac{60\times61}{2}=1830\) and \(S_{30}=\frac{30\times31}{2}=465\). Hence, \(S_{60}:S_{30}=1830:465=122:31\). Option \(61:15\) may appear close, but it is not the simplified ratio of the two sums. Exam tip: you can also cancel common factors directly in \(\frac{60\times61}{30\times31}\) instead of calculating both sums fully.
Frequently asked questions
What is the correct answer to this question?
\(122:31\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{60}=\frac{60\times61}{2}=1830\) and \(S_{30}=\frac{30\times31}{2}=465\). Hence, \(S_{60}:S_{30}=1830:465=122:31\). Option \(61:15\) may appear close, but it is not the simplified ratio of the two sums. Exam tip: you can also cancel common factors directly in \(\frac{60\times61}{30\times31}\) instead of calculating both sums fully.
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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