What is the sum of 151 + 152 + 153 + ... + 210?
Answer and explanation
Correct answer: 10830
The required consecutive sum can be written as S_210 − S_150 because subtracting the first 150 natural numbers leaves 151 through 210. Using S_n = n(n+1)/2, S_210 = 210 × 211/2 = 105 × 211 = 22155, and S_150 = 150 × 151/2 = 75 × 151 = 11325. Hence the sum is 22155 − 11325 = 10830. A second check gives 60 terms, average (151+210)/2 = 180.5, and product 60 × 180.5 = 10830. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
10830
Why is this the correct answer?
The required consecutive sum can be written as S_210 − S_150 because subtracting the first 150 natural numbers leaves 151 through 210. Using S_n = n(n+1)/2, S_210 = 210 × 211/2 = 105 × 211 = 22155, and S_150 = 150 × 151/2 = 75 × 151 = 11325. Hence the sum is 22155 − 11325 = 10830. A second check gives 60 terms, average (151+210)/2 = 180.5, and product 60 × 180.5 = 10830. Therefore option A is correct.
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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