If S_n = 9180, what is the value of n?
Answer and explanation
Correct answer: 135
Use the governing formula S_n = n(n+1)/2 for the sum of the first n natural numbers. Substituting the given value gives n(n+1)/2 = 9180, or n(n+1) = 18360. Since 135 × 136 = 18360, n = 135 satisfies the equation, and therefore S_135 = 135 × 136/2 = 9180. Because n is a positive natural-number index, this is the required value. Option B is correct. The other options do not produce 9180: their consecutive products n(n+1) would be different from 18360, so they cannot satisfy the sum formula.
Frequently asked questions
What is the correct answer to this question?
135
Why is this the correct answer?
Use the governing formula S_n = n(n+1)/2 for the sum of the first n natural numbers. Substituting the given value gives n(n+1)/2 = 9180, or n(n+1) = 18360. Since 135 × 136 = 18360, n = 135 satisfies the equation, and therefore S_135 = 135 × 136/2 = 9180. Because n is a positive natural-number index, this is the required value. Option B is correct. The other options do not produce 9180: their consecutive products n(n+1) would be different from 18360, so they cannot satisfy the sum formula.
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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