What is the value of S_144 − 2S_72?
Answer and explanation
Correct answer: 5184
Use S_n = n(n+1)/2 carefully. We get S_144 = 144 × 145/2 = 72 × 145 = 10440, while S_72 = 72 × 73/2 = 2628. Hence 2S_72 = 5256. The required expression is S_144 − 2S_72 = 10440 − 5256 = 5184, so option D is correct. The factor 2 applies to the entire value of S_72 before subtraction; treating it as part of the index or subtracting S_72 only would produce a different result. This ordering explains why the nearby distractors are not valid.
Frequently asked questions
What is the correct answer to this question?
5184
Why is this the correct answer?
Use S_n = n(n+1)/2 carefully. We get S_144 = 144 × 145/2 = 72 × 145 = 10440, while S_72 = 72 × 73/2 = 2628. Hence 2S_72 = 5256. The required expression is S_144 − 2S_72 = 10440 − 5256 = 5184, so option D is correct. The factor 2 applies to the entire value of S_72 before subtraction; treating it as part of the index or subtracting S_72 only would produce a different result. This ordering explains why the nearby distractors are not valid.
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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