If (S_n-S_{n-1}=225), what will be the value of (S_{n+1})?
Answer and explanation
Correct answer: 25651
For the sum of the first n natural numbers, \(S_n-S_{n-1}=n\), because the new term added to \(S_{n-1}\) is n. Hence, \(n=225\). Therefore, \(S_{n+1}=S_{226}=\frac{226\times227}{2}=25651\). Option A may seem close to \(S_{225}\), but the question asks for the next sum, \(S_{226}\). Exam tip: In such questions, identify \(S_n-S_{n-1}\) directly as n.
Frequently asked questions
What is the correct answer to this question?
25651
Why is this the correct answer?
For the sum of the first n natural numbers, \(S_n-S_{n-1}=n\), because the new term added to \(S_{n-1}\) is n. Hence, \(n=225\). Therefore, \(S_{n+1}=S_{226}=\frac{226\times227}{2}=25651\). Option A may seem close to \(S_{225}\), but the question asks for the next sum, \(S_{226}\). Exam tip: In such questions, identify \(S_n-S_{n-1}\) directly as 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.
