If the sum of the first n natural numbers is Sₙ = 10,440, what is the value of n?
Answer and explanation
Correct answer: 144
Use the governing formula for the sum of the first n natural numbers: S_n = n(n + 1)/2. With S_n = 10,440, we obtain n(n + 1) = 20,880. Testing n = 144 gives 144 × 145 = 20,880, so 144 × 145/2 = 10,440. Therefore option C is correct. The nearby alternatives do not satisfy the equation: n = 141 gives 10,011, n = 142 gives 10,153, and n = 145 gives 10,585. Since the sum increases strictly as n increases through positive natural numbers, there cannot be another positive natural-number answer. Direct substitution therefore confirms n = 144 uniquely.
Frequently asked questions
What is the correct answer to this question?
144
Why is this the correct answer?
Use the governing formula for the sum of the first n natural numbers: S_n = n(n + 1)/2. With S_n = 10,440, we obtain n(n + 1) = 20,880. Testing n = 144 gives 144 × 145 = 20,880, so 144 × 145/2 = 10,440. Therefore option C is correct. The nearby alternatives do not satisfy the equation: n = 141 gives 10,011, n = 142 gives 10,153, and n = 145 gives 10,585. Since the sum increases strictly as n increases through positive natural numbers, there cannot be another positive natural-number answer. Direct substitution therefore confirms n = 144 uniquely.
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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