What is the difference between the sums of the first (180) and first (120) natural numbers?
Answer and explanation
Correct answer: 9030
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{180}=\frac{180\times181}{2}=16290\) and \(S_{120}=\frac{120\times121}{2}=7260\). Therefore, the difference is \(16290-7260=9030\). It is also the sum of the integers from \(121\) to \(180\). Exam tip: The difference of two such sums equals the sum of the terms lying between them.
Frequently asked questions
What is the correct answer to this question?
9030
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{180}=\frac{180\times181}{2}=16290\) and \(S_{120}=\frac{120\times121}{2}=7260\). Therefore, the difference is \(16290-7260=9030\). It is also the sum of the integers from \(121\) to \(180\). Exam tip: The difference of two such sums equals the sum of the terms lying 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.
