If (S_n-S_{n-3}=420), what is (n)?
Answer and explanation
Correct answer: \(141\)
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. In \(S_n-S_{n-3}\), only the last three terms remain: \((n-2)+(n-1)+n\). Thus, \(3n-3=420\), so \(3n=423\) and \(n=141\). If \(n=140\), the difference would be \(417\), so it is not correct. Exam tip: In differences of such sums, cancel the common terms and write only the remaining terms.
Frequently asked questions
What is the correct answer to this question?
\(141\)
Why is this the correct answer?
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. In \(S_n-S_{n-3}\), only the last three terms remain: \((n-2)+(n-1)+n\). Thus, \(3n-3=420\), so \(3n=423\) and \(n=141\). If \(n=140\), the difference would be \(417\), so it is not correct. Exam tip: In differences of such sums, cancel the common terms and write only the remaining 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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