If (S_n-S_{n-5}=490), what will be the value of (n)?
Answer and explanation
Correct answer: \(100\)
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. Therefore, \(S_n-S_{n-5}\) leaves only the last five terms: \((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10\). Thus, \(5n-10=490\), so \(5n=500\) and \(n=100\). If \(n=98\), the sum would be \(480\), so it is not correct. Exam tip: \(S_n-S_{n-k}\) contains the \(k\) terms from \(n-k+1\) to \(n\).
Frequently asked questions
What is the correct answer to this question?
\(100\)
Why is this the correct answer?
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. Therefore, \(S_n-S_{n-5}\) leaves only the last five terms: \((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10\). Thus, \(5n-10=490\), so \(5n=500\) and \(n=100\). If \(n=98\), the sum would be \(480\), so it is not correct. Exam tip: \(S_n-S_{n-k}\) contains the \(k\) terms from \(n-k+1\) 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.
