If (S_n=3240), what will be (S_{n+1}-S_n)?
Answer and explanation
Correct answer: \(81\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=3240\), we get \(n=80\). Hence, \(S_{n+1}-S_n=S_{81}-S_{80}=81\), because the next sum includes only the next natural number. \(80\) is a close distractor, but it is the last number included in \(S_{80}\); the added number is \(81\). Exam tip: the difference of consecutive partial sums is always the next term.
Frequently asked questions
What is the correct answer to this question?
\(81\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=3240\), we get \(n=80\). Hence, \(S_{n+1}-S_n=S_{81}-S_{80}=81\), because the next sum includes only the next natural number. \(80\) is a close distractor, but it is the last number included in \(S_{80}\); the added number is \(81\). Exam tip: the difference of consecutive partial sums is always the next term.
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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