Find the value of (S_{35}-S_{19}).
Answer and explanation
Correct answer: 440
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{35}=\frac{35\times36}{2}=630\) and \(S_{19}=\frac{19\times20}{2}=190\). Therefore, \(S_{35}-S_{19}=630-190=440\). It is also the sum of the natural numbers from 20 to 35. Exam tip: \(S_b-S_a\) represents the sum from \(a+1\) to \(b\).
Frequently asked questions
What is the correct answer to this question?
440
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{35}=\frac{35\times36}{2}=630\) and \(S_{19}=\frac{19\times20}{2}=190\). Therefore, \(S_{35}-S_{19}=630-190=440\). It is also the sum of the natural numbers from 20 to 35. Exam tip: \(S_b-S_a\) represents the sum from \(a+1\) to \(b\).
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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