What is the difference between the sums of the first (55) and first (45) natural numbers?
Answer and explanation
Correct answer: 505
The sum of the first 55 natural numbers is
\(S_{55}=\frac{55\times56}{2}=1540\), and the sum of the first 45 natural numbers is
\(S_{45}=\frac{45\times46}{2}=1035\). Therefore, the difference is
\(1540-1035=505\). Although 500 is close, the exact sum of the numbers from 46 to 55 is 505. Exam tip: For such differences, you can directly add the remaining terms from 46 to 55 instead of finding both full sums.
Frequently asked questions
What is the correct answer to this question?
505
Why is this the correct answer?
The sum of the first 55 natural numbers is
\(S_{55}=\frac{55\times56}{2}=1540\), and the sum of the first 45 natural numbers is
\(S_{45}=\frac{45\times46}{2}=1035\). Therefore, the difference is
\(1540-1035=505\). Although 500 is close, the exact sum of the numbers from 46 to 55 is 505. Exam tip: For such differences, you can directly add the remaining terms from 46 to 55 instead of finding both full sums.
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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