If the sum of the first (n) natural numbers is (325), what will (n) be?
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Answer and explanation
Correct answer: 25
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=325\), so \(n(n+1)=650\). Since \(25\times 26=650\), \(n=25\). For \(n=24\), the sum is \(\frac{24\times25}{2}=300\), not 325. Exam tip: check for two consecutive factors of twice the given sum.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=325\), so \(n(n+1)=650\). Since \(25\times 26=650\), \(n=25\). For \(n=24\), the sum is \(\frac{24\times25}{2}=300\), not 325. Exam tip: check for two consecutive factors of twice the given sum.
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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