If (S_{n+1}-S_{n-2}=330), what will be the value of (n)?
Answer and explanation
Correct answer: 110
Here, \(S_k\) denotes the sum of the first \(k\) natural numbers. In \(S_{n+1}-S_{n-2}\), the terms from 1 to \(n-2\) cancel, leaving \((n-1)+n+(n+1)=3n\). Thus, \(3n=330\), so \(n=110\). If 109 were used, the difference would be \(3\times109=327\), not 330. Exam tip: for differences of partial sums, cancel the common initial terms and write the remaining consecutive terms.
Frequently asked questions
What is the correct answer to this question?
110
Why is this the correct answer?
Here, \(S_k\) denotes the sum of the first \(k\) natural numbers. In \(S_{n+1}-S_{n-2}\), the terms from 1 to \(n-2\) cancel, leaving \((n-1)+n+(n+1)=3n\). Thus, \(3n=330\), so \(n=110\). If 109 were used, the difference would be \(3\times109=327\), not 330. Exam tip: for differences of partial sums, cancel the common initial terms and write the remaining consecutive terms.
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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