If (S_{n+1}-S_{n-4}=595), what will be the value of (n)?
Answer and explanation
Correct answer: 120
Here, \(S_k\) denotes the sum of the first \(k\) natural numbers. Therefore, \(S_{n+1}-S_{n-4}\) leaves the five terms from \((n-3)\) to \((n+1)\): \[(n-3)+(n-2)+(n-1)+n+(n+1)=5n-5.\] Thus, \(5n-5=595\), so \(5n=600\) and \(n=120\). If \(n=119\), the sum would be \(590\), not \(595\). Exam tip: In \(S_a-S_b\), write the terms from \(b+1\) to \(a\).
Frequently asked questions
What is the correct answer to this question?
120
Why is this the correct answer?
Here, \(S_k\) denotes the sum of the first \(k\) natural numbers. Therefore, \(S_{n+1}-S_{n-4}\) leaves the five terms from \((n-3)\) to \((n+1)\): \[(n-3)+(n-2)+(n-1)+n+(n+1)=5n-5.\] Thus, \(5n-5=595\), so \(5n=600\) and \(n=120\). If \(n=119\), the sum would be \(590\), not \(595\). Exam tip: In \(S_a-S_b\), write the terms from \(b+1\) to \(a\).
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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