What is the value of S_200 - S_190?
Answer and explanation
Correct answer: 1955
For partial sums of natural numbers, subtracting S_190 from S_200 cancels the common terms 1 through 190. Thus S_200 - S_190 = 191 + 192 + ... + 200. There are 10 terms, the first is 191, and the last is 200. Using the arithmetic-progression sum formula, the result is 10/2 × (191 + 200) = 5 × 391 = 1955. Therefore option A is correct. A frequent mistake is to count 191 through 200 as nine terms instead of ten, or to use 190 as the first remaining term; either error can produce one of the nearby distractors.
Frequently asked questions
What is the correct answer to this question?
1955
Why is this the correct answer?
For partial sums of natural numbers, subtracting S_190 from S_200 cancels the common terms 1 through 190. Thus S_200 - S_190 = 191 + 192 + ... + 200. There are 10 terms, the first is 191, and the last is 200. Using the arithmetic-progression sum formula, the result is 10/2 × (191 + 200) = 5 × 391 = 1955. Therefore option A is correct. A frequent mistake is to count 191 through 200 as nine terms instead of ten, or to use 190 as the first remaining term; either error can produce one of the nearby distractors.
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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