If (S_n=595), what is (S_{n+6}-S_n)?
Answer and explanation
Correct answer: 225
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=595\), we get \(n=34\). Therefore, \(S_{n+6}-S_n=S_{40}-S_{34}=35+36+37+38+39+40=225\). Although 230 may seem close, it does not equal the sum of the next six terms. In exams, first find n and then add only the newly included terms.
Frequently asked questions
What is the correct answer to this question?
225
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=595\), we get \(n=34\). Therefore, \(S_{n+6}-S_n=S_{40}-S_{34}=35+36+37+38+39+40=225\). Although 230 may seem close, it does not equal the sum of the next six terms. In exams, first find n and then add only the newly included terms.
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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