What is obtained by subtracting the sum of the first (10) natural numbers from the sum of the first (25) natural numbers?
Answer and explanation
Correct answer: 270
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{25}=\frac{25\times26}{2}=325\) and \(S_{10}=\frac{10\times11}{2}=55\). Therefore, \(S_{25}-S_{10}=325-55=270\). This is also the sum of the natural numbers from 11 to 25. Getting 260 usually results from an error while calculating one of the two sums. Exam tip: the difference of two consecutive-range sums directly gives the sum of the terms between them.
Frequently asked questions
What is the correct answer to this question?
270
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{25}=\frac{25\times26}{2}=325\) and \(S_{10}=\frac{10\times11}{2}=55\). Therefore, \(S_{25}-S_{10}=325-55=270\). This is also the sum of the natural numbers from 11 to 25. Getting 260 usually results from an error while calculating one of the two sums. Exam tip: the difference of two consecutive-range sums directly gives the sum of the terms between them.
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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