If the sum of the first (n) natural numbers is (2211), what is (n)?
Answer and explanation
Correct answer: 66
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=2211\), so \(n(n+1)=4422\). Since \(66\times67=4422\), \(n=66\). If \(n=67\), the sum would be \(\frac{67\times68}{2}=2278\), not 2211. Exam tip: multiply the given sum by \(2\) and look for two consecutive factors.
Frequently asked questions
What is the correct answer to this question?
66
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=2211\), so \(n(n+1)=4422\). Since \(66\times67=4422\), \(n=66\). If \(n=67\), the sum would be \(\frac{67\times68}{2}=2278\), not 2211. Exam tip: multiply the given sum by \(2\) and look for two consecutive factors.
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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