If (S_{n+3}-S_{n-2}=760), what is the value of (n)?
Answer and explanation
Correct answer: 151
Here, \(S_k\) denotes the sum of the first \(k\) natural numbers. In \(S_{n+3}-S_{n-2}\), the terms from \(1\) to \(n-2\) cancel, leaving \((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5\). Thus, \(5n+5=760\), so \(5n=755\) and \(n=151\). If \(n=152\), the difference would be \(765\), so it is not correct. Exam tip: when subtracting two partial sums, write only the uncancelled consecutive terms.
Frequently asked questions
What is the correct answer to this question?
151
Why is this the correct answer?
Here, \(S_k\) denotes the sum of the first \(k\) natural numbers. In \(S_{n+3}-S_{n-2}\), the terms from \(1\) to \(n-2\) cancel, leaving \((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5\). Thus, \(5n+5=760\), so \(5n=755\) and \(n=151\). If \(n=152\), the difference would be \(765\), so it is not correct. Exam tip: when subtracting two partial sums, write only the uncancelled consecutive 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.
