What is 3 times the difference between S_48 and S_24?
Answer and explanation
Correct answer: 2628
Use the natural-number sum formula S_k = k(k+1)/2. First, S_48 = 48 × 49 / 2 = 1176, and S_24 = 24 × 25 / 2 = 300. Their difference is therefore 1176 - 300 = 876. Multiplying this difference by 3 gives 3 × 876 = 2628. Hence option B is correct. Equivalently, S_48 - S_24 is the sum of the terms 25 through 48; both methods give 876 before the final multiplication. The other options reflect arithmetic errors in computing one of the partial sums or in multiplying 876 by 3.
Frequently asked questions
What is the correct answer to this question?
2628
Why is this the correct answer?
Use the natural-number sum formula S_k = k(k+1)/2. First, S_48 = 48 × 49 / 2 = 1176, and S_24 = 24 × 25 / 2 = 300. Their difference is therefore 1176 - 300 = 876. Multiplying this difference by 3 gives 3 × 876 = 2628. Hence option B is correct. Equivalently, S_48 - S_24 is the sum of the terms 25 through 48; both methods give 876 before the final multiplication. The other options reflect arithmetic errors in computing one of the partial sums or in multiplying 876 by 3.
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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