If (S_n=2145), what will be the value of (S_{2n}-S_n)?
Answer and explanation
Correct answer: 6370
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=2145\), giving \(n=65\), since \(\frac{65\times66}{2}=2145\). Therefore, \(S_{2n}-S_n=S_{130}-S_{65}=\frac{130\times131}{2}-2145=8515-2145=6370\). A value such as 6270 can result from an error in applying the sum formula or in the final subtraction. Exam tip: first determine \(n\) from the given \(S_n\), and then calculate \(S_{2n}\).
Frequently asked questions
What is the correct answer to this question?
6370
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=2145\), giving \(n=65\), since \(\frac{65\times66}{2}=2145\). Therefore, \(S_{2n}-S_n=S_{130}-S_{65}=\frac{130\times131}{2}-2145=8515-2145=6370\). A value such as 6270 can result from an error in applying the sum formula or in the final subtraction. Exam tip: first determine \(n\) from the given \(S_n\), and then calculate \(S_{2n}\).
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.
