What is the value of (S_{120}-S_{80}+S_{40})?
Answer and explanation
Correct answer: 4840
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{120}=\frac{120\times121}{2}=7260\), \(S_{80}=3240\), and \(S_{40}=820\). Therefore, \(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\). The option 4740 can result from an error while adding or subtracting the final \(S_{40}\). In exams, calculate each \(S_n\) separately before substituting.
Frequently asked questions
What is the correct answer to this question?
4840
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{120}=\frac{120\times121}{2}=7260\), \(S_{80}=3240\), and \(S_{40}=820\). Therefore, \(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\). The option 4740 can result from an error while adding or subtracting the final \(S_{40}\). In exams, calculate each \(S_n\) separately before substituting.
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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