If \(S_n=300\), what will be the value of \(n\)?
Answer and explanation
Correct answer: 24
For the sum of the first \(n\) natural numbers, \(S_n=n(n+1)/2\). We need \(n(n+1)/2=300\), so \(n(n+1)=600\). Among the options, \(n=24\) gives \(24\times25=600\), and therefore \(S_{24}=24\times25/2=300\). Hence option B is correct. The equation can also be solved as \(n^2+n-600=0\), which factors as \((n+25)(n-24)=0\); the positive natural-number solution is 24. The other options produce sums different from 300, so they do not satisfy the defining formula.
Frequently asked questions
What is the correct answer to this question?
24
Why is this the correct answer?
For the sum of the first \(n\) natural numbers, \(S_n=n(n+1)/2\). We need \(n(n+1)/2=300\), so \(n(n+1)=600\). Among the options, \(n=24\) gives \(24\times25=600\), and therefore \(S_{24}=24\times25/2=300\). Hence option B is correct. The equation can also be solved as \(n^2+n-600=0\), which factors as \((n+25)(n-24)=0\); the positive natural-number solution is 24. The other options produce sums different from 300, so they do not satisfy the defining formula.
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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