If \(S_n=4095\), what is the correct value of \(n\)?
Answer and explanation
Correct answer: \(90\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Substituting \(n=90\) gives \(\frac{90\times91}{2}=45\times91=4095\), so the correct value is \(90\). For \(n=89\), the sum is \(4005\), making it a close but incorrect option. In exams, verify the value by substituting it into the sum formula.
Frequently asked questions
What is the correct answer to this question?
\(90\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Substituting \(n=90\) gives \(\frac{90\times91}{2}=45\times91=4095\), so the correct value is \(90\). For \(n=89\), the sum is \(4005\), making it a close but incorrect option. In exams, verify the value by substituting it into the sum formula.
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.
