If \(S_n=3240\), what is the value of \(S_{n+8}-S_n\), where \(S_k=1+2+\cdots+k\)?
Answer and explanation
Correct answer: 676
First determine \(n\) from \(S_n=\frac{n(n+1)}2=3240\). Since \(80\cdot81/2=3240\), we have \(n=80\). The difference \(S_{n+8}-S_n\) consists of the next eight terms, from \(n+1\) through \(n+8\), namely 81 through 88. Their sum is an arithmetic-series sum: \(\frac{8(81+88)}2=4\cdot169=676\). Therefore option A is correct. It is important not to include 80 or skip 88; the difference begins at 81 and contains exactly eight terms. The other options reflect such counting or arithmetic errors.
Frequently asked questions
What is the correct answer to this question?
676
Why is this the correct answer?
First determine \(n\) from \(S_n=\frac{n(n+1)}2=3240\). Since \(80\cdot81/2=3240\), we have \(n=80\). The difference \(S_{n+8}-S_n\) consists of the next eight terms, from \(n+1\) through \(n+8\), namely 81 through 88. Their sum is an arithmetic-series sum: \(\frac{8(81+88)}2=4\cdot169=676\). Therefore option A is correct. It is important not to include 80 or skip 88; the difference begins at 81 and contains exactly eight terms. The other options reflect such counting or arithmetic errors.
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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