If the sum of the first n natural numbers is 120, what is n?
Answer and explanation
Correct answer: 15
The governing concept is the sum formula for the first n natural numbers: S = n(n + 1)/2. Set S = 120, so n(n + 1)/2 = 120, which gives n(n + 1) = 240. Testing the positive integer options, n = 15 gives 15 × 16 = 240, and therefore S = 15 × 16 / 2 = 120. Hence option C is correct. The other choices do not satisfy the equation: n = 12 gives 78, n = 14 gives 105, and n = 16 gives 136. Since n counts natural numbers, a positive integer is required; the quadratic equation also confirms the valid root n = 15.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The governing concept is the sum formula for the first n natural numbers: S = n(n + 1)/2. Set S = 120, so n(n + 1)/2 = 120, which gives n(n + 1) = 240. Testing the positive integer options, n = 15 gives 15 × 16 = 240, and therefore S = 15 × 16 / 2 = 120. Hence option C is correct. The other choices do not satisfy the equation: n = 12 gives 78, n = 14 gives 105, and n = 16 gives 136. Since n counts natural numbers, a positive integer is required; the quadratic equation also confirms the valid root n = 15.
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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