Which sum is obtained by adding 76 + 77 + 78 + 79 + 80 to S_75?
Answer and explanation
Correct answer: S_80
The notation S_k means the sum 1 + 2 + ... + k. Therefore S_75 already contains every natural-number term from 1 through 75. Adding 76, 77, 78, 79, and 80 appends exactly the next five terms, without skipping or repeating any number. Hence S_75 + 76 + 77 + 78 + 79 + 80 equals 1 + 2 + ... + 80, which is S_80. Option C is correct. S_78 would include only three of the added terms, S_79 would omit 80, and S_81 would incorrectly add one further term, 81, that does not appear in the expression.
Frequently asked questions
What is the correct answer to this question?
S_80
Why is this the correct answer?
The notation S_k means the sum 1 + 2 + ... + k. Therefore S_75 already contains every natural-number term from 1 through 75. Adding 76, 77, 78, 79, and 80 appends exactly the next five terms, without skipping or repeating any number. Hence S_75 + 76 + 77 + 78 + 79 + 80 equals 1 + 2 + ... + 80, which is S_80. Option C is correct. S_78 would include only three of the added terms, S_79 would omit 80, and S_81 would incorrectly add one further term, 81, that does not appear in the expression.
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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