What is the difference between the sum of the first (120) natural numbers and the sum of the first (80) natural numbers?
Answer and explanation
Correct answer: 4020
The sum of the first 120 natural numbers is
\(S_{120}=\frac{120\times121}{2}=7260\), and the sum of the first 80 natural numbers is
\(S_{80}=\frac{80\times81}{2}=3240\). Therefore, the difference is
\(7260-3240=4020\). It is also the sum of the numbers from 81 to 120. A value such as 4060 can result from taking an incorrect starting or ending term. Exam tip: use \(S_n=\frac{n(n+1)}{2}\) for each sum before subtracting.
Frequently asked questions
What is the correct answer to this question?
4020
Why is this the correct answer?
The sum of the first 120 natural numbers is
\(S_{120}=\frac{120\times121}{2}=7260\), and the sum of the first 80 natural numbers is
\(S_{80}=\frac{80\times81}{2}=3240\). Therefore, the difference is
\(7260-3240=4020\). It is also the sum of the numbers from 81 to 120. A value such as 4060 can result from taking an incorrect starting or ending term. Exam tip: use \(S_n=\frac{n(n+1)}{2}\) for each sum before subtracting.
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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