What is the sum of (11+12+13+\cdots+30)?
Answer and explanation
Correct answer: (410)
The numbers from 11 to 30 form a consecutive arithmetic sequence. A convenient way to add them is to use the sum of the first 30 natural numbers and remove the sum of the first 10 numbers. The formula is \\(S_n=\\frac{n(n+1)}2\\). Thus \\(S_{30}=\\frac{30\\times31}{2}=465\\), and \\(S_{10}=\\frac{10\\times11}{2}=55\\).
The required sum is therefore \\(S_{30}-S_{10}=465-55=410\\). This includes precisely the terms 11 through 30, because the first ten terms, 1 through 10, have been removed. Hence option D is correct. A common mistake is to subtract only the endpoints or to count the terms incorrectly; the difference-of-sums method avoids both errors.
Frequently asked questions
What is the correct answer to this question?
(410)
Why is this the correct answer?
The numbers from 11 to 30 form a consecutive arithmetic sequence. A convenient way to add them is to use the sum of the first 30 natural numbers and remove the sum of the first 10 numbers. The formula is \\(S_n=\\frac{n(n+1)}2\\). Thus \\(S_{30}=\\frac{30\\times31}{2}=465\\), and \\(S_{10}=\\frac{10\\times11}{2}=55\\).
The required sum is therefore \\(S_{30}-S_{10}=465-55=410\\). This includes precisely the terms 11 through 30, because the first ten terms, 1 through 10, have been removed. Hence option D is correct. A common mistake is to subtract only the endpoints or to count the terms incorrectly; the difference-of-sums method avoids both errors.
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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