If (S_{n+5}-S_{n-5}=1205), what will be the value of (n)?
Answer and explanation
Correct answer: 120
Here, \(S_{n+5}-S_{n-5}\) represents the sum of 10 consecutive natural numbers from \((n-4)\) to \((n+5)\). Therefore, \(S_{n+5}-S_{n-5}=10n+5\). So, \(10n+5=1205\), which gives \(10n=1200\) and hence \(n=120\). If \(n=121\), the sum would be \(1215\), not the given value. Exam tip: In such differences, list the first and last remaining terms to verify the number of terms.
Frequently asked questions
What is the correct answer to this question?
120
Why is this the correct answer?
Here, \(S_{n+5}-S_{n-5}\) represents the sum of 10 consecutive natural numbers from \((n-4)\) to \((n+5)\). Therefore, \(S_{n+5}-S_{n-5}=10n+5\). So, \(10n+5=1205\), which gives \(10n=1200\) and hence \(n=120\). If \(n=121\), the sum would be \(1215\), not the given value. Exam tip: In such differences, list the first and last remaining terms to verify the number of 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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