If (S_{n+2}-S_{n-3}=625), what is the value of (n)?
Answer and explanation
Correct answer: 125
In \(S_{n+2}-S_{n-3}\), all terms up to \((n-3)\) cancel. The five remaining terms are \((n-2)+(n-1)+n+(n+1)+(n+2)=5n\). Hence, \(5n=625\), giving \(n=125\). If \(n=126\), the difference would be \(630\), so it is not correct. Exam tip: In differences of partial sums, write and add the uncancelled terms between the two indices.
Frequently asked questions
What is the correct answer to this question?
125
Why is this the correct answer?
In \(S_{n+2}-S_{n-3}\), all terms up to \((n-3)\) cancel. The five remaining terms are \((n-2)+(n-1)+n+(n+1)+(n+2)=5n\). Hence, \(5n=625\), giving \(n=125\). If \(n=126\), the difference would be \(630\), so it is not correct. Exam tip: In differences of partial sums, write and add the uncancelled terms between the two indices.
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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