If the sum of the first n natural numbers is 91, choose n.
Answer and explanation
Correct answer: 13
Use the governing equation S_n = n(n + 1)/2. The question states that S_n = 91, so n(n + 1)/2 = 91. Multiplying by 2 gives n(n + 1) = 182. Among the choices, n = 13 gives 13 × 14 = 182, and therefore 13 × 14 / 2 = 91. Thus option B is correct. A quick check of nearby values is useful: S_12 = 12 × 13 / 2 = 78, while S_14 = 14 × 15 / 2 = 105, so 91 lies exactly at n = 13. The answer is not 14 merely because 14 appears as the next factor in the product.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
Use the governing equation S_n = n(n + 1)/2. The question states that S_n = 91, so n(n + 1)/2 = 91. Multiplying by 2 gives n(n + 1) = 182. Among the choices, n = 13 gives 13 × 14 = 182, and therefore 13 × 14 / 2 = 91. Thus option B is correct. A quick check of nearby values is useful: S_12 = 12 × 13 / 2 = 78, while S_14 = 14 × 15 / 2 = 105, so 91 lies exactly at n = 13. The answer is not 14 merely because 14 appears as the next factor in the product.
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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