If (S_n=4560), what is the value of (S_{n+5}-S_n)?
Answer and explanation
Correct answer: 490
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=4560\), we get \(n=95\). Hence, \(S_{n+5}-S_n\) is the sum of the next five natural numbers: \(96+97+98+99+100=490\). The value \(495\) would result if 101 were also included. Exam tip: \(S_{n+k}-S_n\) always represents the sum of terms from \(n+1\) to \(n+k\).
Frequently asked questions
What is the correct answer to this question?
490
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=4560\), we get \(n=95\). Hence, \(S_{n+5}-S_n\) is the sum of the next five natural numbers: \(96+97+98+99+100=490\). The value \(495\) would result if 101 were also included. Exam tip: \(S_{n+k}-S_n\) always represents 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.
