If the sum of the first (n) natural numbers is (990), what is (n)?
Answer and explanation
Correct answer: 44
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=990\), so \(n(n+1)=1980\). Since \(44\times45=1980\), \(n=44\). For the closest distractor, \(n=43\) gives \(\frac{43\times44}{2}=946\), not 990. Exam tip: for such questions, look for two consecutive factors of \(2S\).
Frequently asked questions
What is the correct answer to this question?
44
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=990\), so \(n(n+1)=1980\). Since \(44\times45=1980\), \(n=44\). For the closest distractor, \(n=43\) gives \(\frac{43\times44}{2}=946\), not 990. Exam tip: for such questions, look for two consecutive factors of \(2S\).
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.
