If (S_n=3655), what will be (S_n-S_{n-4})?
Answer and explanation
Correct answer: 334
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=3655\), we get \(n=85\), since \(\frac{85\times86}{2}=3655\). Therefore, \(S_n-S_{n-4}=S_{85}-S_{81}\), which is the sum of the last four terms: \(82+83+84+85=334\). The value 330 would result from adding \(81+82+83+84\), which is not the required set of final four terms. Exam tip: \(S_n-S_{n-r}\) equals the sum of the last r terms up to n.
Frequently asked questions
What is the correct answer to this question?
334
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=3655\), we get \(n=85\), since \(\frac{85\times86}{2}=3655\). Therefore, \(S_n-S_{n-4}=S_{85}-S_{81}\), which is the sum of the last four terms: \(82+83+84+85=334\). The value 330 would result from adding \(81+82+83+84\), which is not the required set of final four terms. Exam tip: \(S_n-S_{n-r}\) equals the sum of the last r terms up to n.
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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