What is the ratio of the sum of the first (30) natural numbers to the sum of the first (20) natural numbers?
Answer and explanation
Correct answer: 31:14
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 \(S_{20}=\frac{20\times21}{2}=210\). Therefore, \(S_{30}:S_{20}=465:210=31:14\). In 31:15, the second term does not match the simplified ratio. Exam tip: always divide both terms of a ratio by their greatest common factor to obtain the simplest form.
Frequently asked questions
What is the correct answer to this question?
31:14
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 \(S_{20}=\frac{20\times21}{2}=210\). Therefore, \(S_{30}:S_{20}=465:210=31:14\). In 31:15, the second term does not match the simplified ratio. Exam tip: always divide both terms of a ratio by their greatest common factor to obtain the simplest form.
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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