What is half of the sum of the first (84) natural numbers?
Answer and explanation
Correct answer: 1785
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(S_{84}=\frac{84\times85}{2}=3570\). Half of this sum is \(\frac{3570}{2}=1785\), so option B is correct. A nearby value such as \(1815\) may look plausible, but it is not half of the required sum. Exam tip: first find the total using \(n(n+1)/2\), then apply the fraction asked for—in this case, one-half.
Frequently asked questions
What is the correct answer to this question?
1785
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). Thus, \(S_{84}=\frac{84\times85}{2}=3570\). Half of this sum is \(\frac{3570}{2}=1785\), so option B is correct. A nearby value such as \(1815\) may look plausible, but it is not half of the required sum. Exam tip: first find the total using \(n(n+1)/2\), then apply the fraction asked for—in this case, one-half.
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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