What sum is obtained by adding 53 + 54 + 55 to 1 + 2 + ⋯ + 52?
Answer and explanation
Correct answer: 1540
The governing idea is that consecutive terms can be joined into one longer first-n sum. The expression 1 + 2 + ⋯ + 52 already equals S₅₂. Adding 53, 54, and 55 extends the sequence without a gap, so the complete expression is S₅₅. Apply Sₙ = n(n + 1)/2: S₅₅ = 55 × 56/2 = 55 × 28 = 1540. Therefore option A is correct. It would be incorrect to add the indices 52, 53, 54, and 55, because these numbers are terms included in the same sum rather than separate indices to be combined. The other choices are plausible numerical distractors caused by selecting the wrong final term or making a multiplication error.
Frequently asked questions
What is the correct answer to this question?
1540
Why is this the correct answer?
The governing idea is that consecutive terms can be joined into one longer first-n sum. The expression 1 + 2 + ⋯ + 52 already equals S₅₂. Adding 53, 54, and 55 extends the sequence without a gap, so the complete expression is S₅₅. Apply Sₙ = n(n + 1)/2: S₅₅ = 55 × 56/2 = 55 × 28 = 1540. Therefore option A is correct. It would be incorrect to add the indices 52, 53, 54, and 55, because these numbers are terms included in the same sum rather than separate indices to be combined. The other choices are plausible numerical distractors caused by selecting the wrong final term or making a multiplication error.
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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