If (S_n=4950), what will (n) be?
Answer and explanation
Correct answer: 99
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=4950\), so \(n(n+1)=9900\). Since \(99\times100=9900\), \(n=99\). For \(n=100\), the sum would be \(5050\), not 4950. Exam tip: Multiply the given sum by 2 and look for two consecutive numbers whose product equals the result.
Frequently asked questions
What is the correct answer to this question?
99
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=4950\), so \(n(n+1)=9900\). Since \(99\times100=9900\), \(n=99\). For \(n=100\), the sum would be \(5050\), not 4950. Exam tip: Multiply the given sum by 2 and look for two consecutive numbers whose product equals the result.
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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