For which (n) will the sum of the first (n) natural numbers be (66)?
Answer and explanation
Correct answer: 11
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). So, \(\frac{n(n+1)}{2}=66\), giving \(n(n+1)=132\). Since \(11\times12=132\), \(n=11\). For \(n=12\), the sum is \(\frac{12\times13}{2}=78\), not 66. Exam tip: look for two consecutive numbers whose product equals \(2S\).
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). So, \(\frac{n(n+1)}{2}=66\), giving \(n(n+1)=132\). Since \(11\times12=132\), \(n=11\). For \(n=12\), the sum is \(\frac{12\times13}{2}=78\), not 66. Exam tip: look for two consecutive numbers whose product equals \(2S\).
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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