If (S_n=325), what will (n) be?
Answer and explanation
Correct answer: 25
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=325\), so \(n(n+1)=650\). Since \(25\times26=650\), \(n=25\). For \(n=24\), the sum is \(300\), so it is a close but incorrect option. Exam tip: look for consecutive factors of 650 in such questions.
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 \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=325\), so \(n(n+1)=650\). Since \(25\times26=650\), \(n=25\). For \(n=24\), the sum is \(300\), so it is a close but incorrect option. Exam tip: look for consecutive factors of 650 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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