What will be the sum of the first 12 natural numbers?
Answer and explanation
Correct answer: 78
This is a direct application of the triangular-number formula S_n = n(n + 1)/2, which gives the sum of 1 through n. Since the question asks for the first 12 natural numbers, put n = 12: S_12 = 12 × 13 / 2. Dividing 12 by 2 first gives 6, and 6 × 13 = 78. Hence option C is the unique correct answer. The other values do not satisfy the formula: 72 is too low, 74 is not the required triangular number, and 82 is too high. The phrase first 12 means the terms 1, 2, ..., 12, not twelve times 12 and not a sequence beginning with zero.
Frequently asked questions
What is the correct answer to this question?
78
Why is this the correct answer?
This is a direct application of the triangular-number formula S_n = n(n + 1)/2, which gives the sum of 1 through n. Since the question asks for the first 12 natural numbers, put n = 12: S_12 = 12 × 13 / 2. Dividing 12 by 2 first gives 6, and 6 × 13 = 78. Hence option C is the unique correct answer. The other values do not satisfy the formula: 72 is too low, 74 is not the required triangular number, and 82 is too high. The phrase first 12 means the terms 1, 2, ..., 12, not twelve times 12 and not a sequence beginning with zero.
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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