Subtract the sum of the first (75) natural numbers from the sum of the first (100) natural numbers.
Answer and explanation
Correct answer: 2200
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{100}=\frac{100\times101}{2}=5050\) and \(S_{75}=\frac{75\times76}{2}=2850\). The required difference is \(5050-2850=2200\), so option B is correct. It is also the sum of the integers from 76 to 100. Option 2250 can result from an incorrect value of \(S_{75}\) or a subtraction error. Exam tip: interpret \(S_b-S_a\) as the sum of terms from \(a+1\) to \(b\).
Frequently asked questions
What is the correct answer to this question?
2200
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{100}=\frac{100\times101}{2}=5050\) and \(S_{75}=\frac{75\times76}{2}=2850\). The required difference is \(5050-2850=2200\), so option B is correct. It is also the sum of the integers from 76 to 100. Option 2250 can result from an incorrect value of \(S_{75}\) or a subtraction error. Exam tip: interpret \(S_b-S_a\) as the sum of terms 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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