If the sum of the first (n) natural numbers is (1540), what is (n)?
Answer and explanation
Correct answer: 55
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=1540\), so \(n(n+1)=3080\). Since \(55\times56=3080\), \(n=55\). For example, if \(n=54\), the sum is \(\frac{54\times55}{2}=1485\), not 1540. Exam tip: find two consecutive factors of \(2S\) in such questions.
Frequently asked questions
What is the correct answer to this question?
55
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=1540\), so \(n(n+1)=3080\). Since \(55\times56=3080\), \(n=55\). For example, if \(n=54\), the sum is \(\frac{54\times55}{2}=1485\), not 1540. Exam tip: find two consecutive factors of \(2S\) in such questions.
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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