Find the sum of natural numbers from (181) to (240).
Answer and explanation
Correct answer: (12630)
The required numbers form a consecutive sequence beginning at 181 and ending at 240. The sum of numbers from 181 to 240 can be found efficiently by subtracting the sum through 180 from the sum through 240. Using \\(S_n=\frac{n(n+1)}{2}\\) ensures that both endpoints are handled correctly.
We have \\(S_{240}=\frac{240\times241}{2}=28920\\) and \\(S_{180}=\frac{180\times181}{2}=16290\\). Therefore, the required sum is \\(28920-16290=12630\\). As a second check, there are 60 terms and their average is \\(\frac{181+240}{2}=210.5\\), so the sum is \\(60\times210.5=12630\\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
(12630)
Why is this the correct answer?
The required numbers form a consecutive sequence beginning at 181 and ending at 240. The sum of numbers from 181 to 240 can be found efficiently by subtracting the sum through 180 from the sum through 240. Using \\(S_n=\frac{n(n+1)}{2}\\) ensures that both endpoints are handled correctly.
We have \\(S_{240}=\frac{240\times241}{2}=28920\\) and \\(S_{180}=\frac{180\times181}{2}=16290\\). Therefore, the required sum is \\(28920-16290=12630\\). As a second check, there are 60 terms and their average is \\(\frac{181+240}{2}=210.5\\), so the sum is \\(60\times210.5=12630\\). 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.
