If (S_n-S_{n-6}=813), what will be the value of (n)?
Answer and explanation
Correct answer: 138
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_n-S_{n-6}\) is the sum of the last six numbers: \((n-5),(n-4),\ldots,n\). Hence, \(S_n-S_{n-6}=6n-15\). Using the given condition, \(6n-15=813\), so \(6n=828\) and \(n=138\). Therefore, option D is correct. If \(n=137\), the difference is \(807\), not 813. Exam tip: Interpret \(S_n-S_{n-k}\) as the sum of the last \(k\) terms to solve quickly.
Frequently asked questions
What is the correct answer to this question?
138
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_n-S_{n-6}\) is the sum of the last six numbers: \((n-5),(n-4),\ldots,n\). Hence, \(S_n-S_{n-6}=6n-15\). Using the given condition, \(6n-15=813\), so \(6n=828\) and \(n=138\). Therefore, option D is correct. If \(n=137\), the difference is \(807\), not 813. Exam tip: Interpret \(S_n-S_{n-k}\) as the sum of the last \(k\) terms to solve quickly.
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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