How much is the sum of natural numbers from (201) to (250)?
Answer and explanation
Correct answer: (11275)
To add consecutive natural numbers from 201 to 250, use the sum formula for an initial segment and subtract the numbers up to 200. The formula is \\(S_n=\frac{n(n+1)}{2}\\). Subtracting \\(S_{200}\\) removes 1 through 200 and leaves exactly 201 through 250, so no endpoint is missed.
Calculate \\(S_{250}=\frac{250\times251}{2}=31375\\), and \\(S_{200}=\frac{200\times201}{2}=20100\\). Therefore, the required sum is \\(S_{250}-S_{200}=31375-20100=11275\\). A quick check uses 50 terms with average \\(\frac{201+250}{2}=225.5\\), giving \\(50\times225.5=11275\\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
(11275)
Why is this the correct answer?
To add consecutive natural numbers from 201 to 250, use the sum formula for an initial segment and subtract the numbers up to 200. The formula is \\(S_n=\frac{n(n+1)}{2}\\). Subtracting \\(S_{200}\\) removes 1 through 200 and leaves exactly 201 through 250, so no endpoint is missed.
Calculate \\(S_{250}=\frac{250\times251}{2}=31375\\), and \\(S_{200}=\frac{200\times201}{2}=20100\\). Therefore, the required sum is \\(S_{250}-S_{200}=31375-20100=11275\\). A quick check uses 50 terms with average \\(\frac{201+250}{2}=225.5\\), giving \\(50\times225.5=11275\\). Hence option A is correct.
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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