If the sum of the first n natural numbers is 210, what is n?
Answer and explanation
Correct answer: 20
Use the governing formula S = n(n + 1)/2 for the sum of the first n natural numbers. With S = 210, we have n(n + 1)/2 = 210, so n(n + 1) = 420. For n = 20, the product is 20 × 21 = 420, and the sum is 20 × 21 / 2 = 210. Thus option C is correct. Checking the nearby distractors confirms the result: n = 18 gives 171, n = 19 gives 190, and n = 21 gives 231. Since n represents a count, the positive integer solution is required. Algebraically, n² + n − 420 = 0 factors as (n − 20)(n + 21) = 0; the admissible root is n = 20.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Use the governing formula S = n(n + 1)/2 for the sum of the first n natural numbers. With S = 210, we have n(n + 1)/2 = 210, so n(n + 1) = 420. For n = 20, the product is 20 × 21 = 420, and the sum is 20 × 21 / 2 = 210. Thus option C is correct. Checking the nearby distractors confirms the result: n = 18 gives 171, n = 19 gives 190, and n = 21 gives 231. Since n represents a count, the positive integer solution is required. Algebraically, n² + n − 420 = 0 factors as (n − 20)(n + 21) = 0; the admissible root is n = 20.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
