What is the value of (S_{22}+S_{17})?
Answer and explanation
Correct answer: 406
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{22}=\frac{22\times23}{2}=253\) and \(S_{17}=\frac{17\times18}{2}=153\). Therefore, \(S_{22}+S_{17}=253+153=406\). Although 396 is close, it is not obtained by adding the two correct sums. Exam tip: whenever \(S_n\) appears, use \(\frac{n(n+1)}{2}\) directly.
Frequently asked questions
What is the correct answer to this question?
406
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{22}=\frac{22\times23}{2}=253\) and \(S_{17}=\frac{17\times18}{2}=153\). Therefore, \(S_{22}+S_{17}=253+153=406\). Although 396 is close, it is not obtained by adding the two correct sums. Exam tip: whenever \(S_n\) appears, use \(\frac{n(n+1)}{2}\) directly.
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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