What is the difference between the sums of the first (120) and first (85) natural numbers?
Answer and explanation
Correct answer: 3605
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{120}=\frac{120\times121}{2}=7260\) and \(S_{85}=\frac{85\times86}{2}=3655\). Therefore, the difference is \(7260-3655=3605\). An answer such as 3585 usually results from a minor subtraction or multiplication error. Exam tip: this difference can also be found directly as the sum of the integers from \(86\) to \(120\).
Frequently asked questions
What is the correct answer to this question?
3605
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{120}=\frac{120\times121}{2}=7260\) and \(S_{85}=\frac{85\times86}{2}=3655\). Therefore, the difference is \(7260-3655=3605\). An answer such as 3585 usually results from a minor subtraction or multiplication error. Exam tip: this difference can also be found directly as the sum of the integers from \(86\) to \(120\).
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.
