If (S_n=11175), what will be (S_n-S_{n-4})?
Answer and explanation
Correct answer: 590
Using \(S_n=\frac{n(n+1)}{2}\) and \(S_n=11175\), we get \(n=149\). Hence, \(S_n-S_{n-4}=S_{149}-S_{145}\), which is the sum of the natural numbers from 146 to 149: \(146+147+148+149=590\). Therefore, 590 is correct. A value such as 580 can result from taking one of the last four terms incorrectly. Exam tip: \(S_n-S_{n-k}\) always represents the sum of the last \(k\) terms.
Frequently asked questions
What is the correct answer to this question?
590
Why is this the correct answer?
Using \(S_n=\frac{n(n+1)}{2}\) and \(S_n=11175\), we get \(n=149\). Hence, \(S_n-S_{n-4}=S_{149}-S_{145}\), which is the sum of the natural numbers from 146 to 149: \(146+147+148+149=590\). Therefore, 590 is correct. A value such as 580 can result from taking one of the last four terms incorrectly. Exam tip: \(S_n-S_{n-k}\) always represents the sum of the last \(k\) 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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