If (S_n=5995), what will be the value of (S_{n-8})?
Answer and explanation
Correct answer: 5151
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=5995\), we get \(n=109\), since \(\frac{109\times110}{2}=5995\). Hence, \(n-8=101\), so \(S_{n-8}=S_{101}=\frac{101\times102}{2}=5151\). The value \(5050\) is \(S_{100}\), so it is close but not correct. Exam tip: first determine n from the given sum, then calculate the sum for the required index.
Frequently asked questions
What is the correct answer to this question?
5151
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=5995\), we get \(n=109\), since \(\frac{109\times110}{2}=5995\). Hence, \(n-8=101\), so \(S_{n-8}=S_{101}=\frac{101\times102}{2}=5151\). The value \(5050\) is \(S_{100}\), so it is close but not correct. Exam tip: first determine n from the given sum, then calculate the sum for the required index.
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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