If (S_n=5050), what is the value of (S_{n+4}-S_n)?
Answer and explanation
Correct answer: 410
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(S_n=5050\), we get \(\frac{n(n+1)}{2}=5050\), so \(n=100\). Hence, \(S_{n+4}-S_n\) is the sum of the next four terms: \(101+102+103+104=410\). The value 406 is only the sum of the next three terms, \(101+102+103\). Exam tip: write \(S_{n+k}-S_n\) as the sum of terms from \(n+1\) to \(n+k\).
Frequently asked questions
What is the correct answer to this question?
410
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(S_n=5050\), we get \(\frac{n(n+1)}{2}=5050\), so \(n=100\). Hence, \(S_{n+4}-S_n\) is the sum of the next four terms: \(101+102+103+104=410\). The value 406 is only the sum of the next three terms, \(101+102+103\). Exam tip: write \(S_{n+k}-S_n\) as the sum of terms from \(n+1\) to \(n+k\).
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.
