What is the value of (S_{44}-S_{30})?
Answer and explanation
Correct answer: 525
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{44}=\frac{44\times45}{2}=990\) and \(S_{30}=\frac{30\times31}{2}=465\). Therefore, \(S_{44}-S_{30}=990-465=525\). This difference is the sum of the natural numbers from 31 to 44. A nearby option such as 535 can result from an arithmetic error in addition or subtraction. Exam tip: interpret \(S_{44}-S_{30}\) directly as the sum from 31 to 44.
Frequently asked questions
What is the correct answer to this question?
525
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{44}=\frac{44\times45}{2}=990\) and \(S_{30}=\frac{30\times31}{2}=465\). Therefore, \(S_{44}-S_{30}=990-465=525\). This difference is the sum of the natural numbers from 31 to 44. A nearby option such as 535 can result from an arithmetic error in addition or subtraction. Exam tip: interpret \(S_{44}-S_{30}\) directly as the sum from 31 to 44.
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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