For which (n) will (S_n-S_{n-1}=62)?
Answer and explanation
Correct answer: 62
For the sum of the first n natural numbers, \(S_n=\frac{n(n+1)}{2}\). Therefore, \(S_n-S_{n-1}=n\), since the difference leaves only the newly added term n. Given \(S_n-S_{n-1}=62\), we get \(n=62\). If n were 61, the difference would be 61, not 62. Exam tip: The difference between two consecutive partial sums is always the newly added term of the sequence.
Frequently asked questions
What is the correct answer to this question?
62
Why is this the correct answer?
For the sum of the first n natural numbers, \(S_n=\frac{n(n+1)}{2}\). Therefore, \(S_n-S_{n-1}=n\), since the difference leaves only the newly added term n. Given \(S_n-S_{n-1}=62\), we get \(n=62\). If n were 61, the difference would be 61, not 62. Exam tip: The difference between two consecutive partial sums is always the newly added term of the sequence.
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.
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