If (S_n-S_{n-3}=348), what is the value of (S_n)?
Answer and explanation
Correct answer: 6903
Here, \(S_n-S_{n-3}\) represents the sum of the three consecutive natural numbers \(n\), \(n-1\), and \(n-2\). Thus, \(S_n-S_{n-3}=n+(n-1)+(n-2)=3n-3\). From \(3n-3=348\), we get \(n=117\). Therefore, \(S_{117}=\frac{117\times118}{2}=6903\). Hence, option C is correct. The value 6786 may appear close to \(S_{116}\), but the required value is for \(n=117\). Exam tip: \(S_n-S_{n-k}\) is the sum of the last \(k\) terms.
Frequently asked questions
What is the correct answer to this question?
6903
Why is this the correct answer?
Here, \(S_n-S_{n-3}\) represents the sum of the three consecutive natural numbers \(n\), \(n-1\), and \(n-2\). Thus, \(S_n-S_{n-3}=n+(n-1)+(n-2)=3n-3\). From \(3n-3=348\), we get \(n=117\). Therefore, \(S_{117}=\frac{117\times118}{2}=6903\). Hence, option C is correct. The value 6786 may appear close to \(S_{116}\), but the required value is for \(n=117\). Exam tip: \(S_n-S_{n-k}\) is the sum of 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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