Find the value of \(S_{30}-S_{18}\).
Answer and explanation
Correct answer: 294
Here \(S_n\) denotes the sum of the first \(n\) natural numbers, so \(S_n=n(n+1)/2\). Calculate each required sum separately: \(S_{30}=30\times31/2=465\), while \(S_{18}=18\times19/2=171\). Their difference is therefore \(465-171=294\). Hence option B is correct. A useful equivalent interpretation is that the difference contains the terms from 19 through 30: \(19+20+\cdots+30\). There are 12 terms and their average is \((19+30)/2=24.5\), giving \(12\times24.5=294\). The other options arise from incorrect multiplication, subtraction, or endpoint handling.
Frequently asked questions
What is the correct answer to this question?
294
Why is this the correct answer?
Here \(S_n\) denotes the sum of the first \(n\) natural numbers, so \(S_n=n(n+1)/2\). Calculate each required sum separately: \(S_{30}=30\times31/2=465\), while \(S_{18}=18\times19/2=171\). Their difference is therefore \(465-171=294\). Hence option B is correct. A useful equivalent interpretation is that the difference contains the terms from 19 through 30: \(19+20+\cdots+30\). There are 12 terms and their average is \((19+30)/2=24.5\), giving \(12\times24.5=294\). The other options arise from incorrect multiplication, subtraction, or endpoint handling.
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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