If (S_{2n}=4095), what is the value of (n)?
Answer and explanation
Correct answer: 45
The sum of the first \(r\) natural numbers is \(S_r=\frac{r(r+1)}{2}\). Given \(S_{2n}=4095\), we have \(\frac{2n(2n+1)}{2}=4095\). Since \(4095=\frac{90\times91}{2}=S_{90}\), \(2n=90\), so \(n=45\). If \(n=46\), then the index would be 92, whose sum is not 4095. Exam tip: first identify the index corresponding to the given sum \(S_r\).
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
The sum of the first \(r\) natural numbers is \(S_r=\frac{r(r+1)}{2}\). Given \(S_{2n}=4095\), we have \(\frac{2n(2n+1)}{2}=4095\). Since \(4095=\frac{90\times91}{2}=S_{90}\), \(2n=90\), so \(n=45\). If \(n=46\), then the index would be 92, whose sum is not 4095. Exam tip: first identify the index corresponding to the given sum \(S_r\).
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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