A teacher asks for the sum of roll numbers from 1 to 31. What is the correct answer?
Answer and explanation
Correct answer: 496
The roll numbers form the consecutive sequence 1, 2, 3, ..., 31. Therefore this is the sum of the first 31 natural numbers, using S_n = n(n + 1)/2. Substitute n = 31: S_31 = 31 × 32 / 2. Since 32/2 = 16, the result is 31 × 16 = 496. Hence option B is correct. A pairing check gives the same answer: 1 + 31, 2 + 30, and so on make 15 pairs of 32, with 16 remaining, so 15 × 32 + 16 = 496. The other options differ by 10 or 20 and reflect arithmetic or pairing mistakes.
Frequently asked questions
What is the correct answer to this question?
496
Why is this the correct answer?
The roll numbers form the consecutive sequence 1, 2, 3, ..., 31. Therefore this is the sum of the first 31 natural numbers, using S_n = n(n + 1)/2. Substitute n = 31: S_31 = 31 × 32 / 2. Since 32/2 = 16, the result is 31 × 16 = 496. Hence option B is correct. A pairing check gives the same answer: 1 + 31, 2 + 30, and so on make 15 pairs of 32, with 16 remaining, so 15 × 32 + 16 = 496. The other options differ by 10 or 20 and reflect arithmetic or pairing mistakes.
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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