In a game, marks from (1) to (20) are scored in the first (20) stages, and (0) marks in the next (5) stages. What is the total score?
Answer and explanation
Correct answer: 210
The marks in the first 20 stages are the sum of natural numbers from 1 to 20: \(S_{20}=\frac{20\times21}{2}=210\). The next 5 stages contribute 0 marks, so they do not change the total. Therefore, the total score is 210. A common error is getting 200 by forgetting the \(n+1\) factor in the sum formula. Exam tip: use \(\frac{n(n+1)}{2}\) for the sum from 1 to \(n\).
Frequently asked questions
What is the correct answer to this question?
210
Why is this the correct answer?
The marks in the first 20 stages are the sum of natural numbers from 1 to 20: \(S_{20}=\frac{20\times21}{2}=210\). The next 5 stages contribute 0 marks, so they do not change the total. Therefore, the total score is 210. A common error is getting 200 by forgetting the \(n+1\) factor in the sum formula. Exam tip: use \(\frac{n(n+1)}{2}\) for the sum from 1 to \(n\).
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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