If (S_n=1128), what will (n) be?
Answer and explanation
Correct answer: 47
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(\frac{n(n+1)}{2}=1128\), so \(n(n+1)=2256\). Since \(47\times48=2256\), \(n=47\). Option 48 is not correct because \(\frac{48\times49}{2}=1176\). Exam tip: for such questions, look for two consecutive factors whose product is twice the given sum.
Frequently asked questions
What is the correct answer to this question?
47
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(\frac{n(n+1)}{2}=1128\), so \(n(n+1)=2256\). Since \(47\times48=2256\), \(n=47\). Option 48 is not correct because \(\frac{48\times49}{2}=1176\). Exam tip: for such questions, look for two consecutive factors whose product is twice the given sum.
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.
