If (S_n-S_{n-4}=454), what is the value of (n)?
Answer and explanation
Correct answer: 115
Here, \(S_n-S_{n-4}\) represents the sum of the last four natural numbers from \((n-3)\) to \(n\). Thus, \((n-3)+(n-2)+(n-1)+n=4n-6\). Hence, \(4n-6=454\), so \(4n=460\) and \(n=115\). If \(n=114\), the sum is \(450\), so it is the closest option but not correct. Exam tip: In \(S_n-S_{n-k}\), add the last \(k\) terms.
Frequently asked questions
What is the correct answer to this question?
115
Why is this the correct answer?
Here, \(S_n-S_{n-4}\) represents the sum of the last four natural numbers from \((n-3)\) to \(n\). Thus, \((n-3)+(n-2)+(n-1)+n=4n-6\). Hence, \(4n-6=454\), so \(4n=460\) and \(n=115\). If \(n=114\), the sum is \(450\), so it is the closest option but not correct. Exam tip: In \(S_n-S_{n-k}\), add the last \(k\) 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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