If (S_n=3240), what will be the value of (S_{n-4})?
Answer and explanation
Correct answer: 2926
For the sum of the first n natural numbers, \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=3240\), we get \(n=80\). Therefore, \(S_{n-4}=S_{76}\). Now \(S_{76}=S_{80}-(77+78+79+80)=3240-314=2926\). Option 2916 results from subtracting the last four terms incorrectly. Exam tip: To find \(S_{n-k}\), subtract the last k terms from \(S_n\).
Frequently asked questions
What is the correct answer to this question?
2926
Why is this the correct answer?
For the sum of the first n natural numbers, \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=3240\), we get \(n=80\). Therefore, \(S_{n-4}=S_{76}\). Now \(S_{76}=S_{80}-(77+78+79+80)=3240-314=2926\). Option 2916 results from subtracting the last four terms incorrectly. Exam tip: To find \(S_{n-k}\), subtract the last k terms from \(S_n\).
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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