What is the sum of natural numbers from 21 to 35?
Answer and explanation
Correct answer: 420
The required terms are 21, 22, ..., 35. One efficient method is to subtract the sum of the first 20 natural numbers from the sum of the first 35 natural numbers. Using \(S_n=n(n+1)/2\), we get \(S_{35}=35\times36/2=630\) and \(S_{20}=20\times21/2=210\). Hence the requested sum is \(S_{35}-S_{20}=630-210=420\). Therefore option D is correct. Equivalently, there are 15 terms, their first and last terms have average \((21+35)/2=28\), and \(15\times28=420\). The other choices result from arithmetic or endpoint-counting errors.
Frequently asked questions
What is the correct answer to this question?
420
Why is this the correct answer?
The required terms are 21, 22, ..., 35. One efficient method is to subtract the sum of the first 20 natural numbers from the sum of the first 35 natural numbers. Using \(S_n=n(n+1)/2\), we get \(S_{35}=35\times36/2=630\) and \(S_{20}=20\times21/2=210\). Hence the requested sum is \(S_{35}-S_{20}=630-210=420\). Therefore option D is correct. Equivalently, there are 15 terms, their first and last terms have average \((21+35)/2=28\), and \(15\times28=420\). The other choices result from arithmetic or endpoint-counting 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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