What remains when (1+2+\cdots+50) is subtracted from (1+2+\cdots+80)?
Answer and explanation
Correct answer: 1965
The sum of the first 80 natural numbers is \(\frac{80\times81}{2}=3240\), and the sum of the first 50 natural numbers is \(\frac{50\times51}{2}=1275\). Therefore, the required difference is \(3240-1275=1965\). Equivalently, it is the sum of the integers from 51 to 80. Exam tip: use \(n(n+1)/2\) carefully for both sums to avoid a close error such as 1975.
Frequently asked questions
What is the correct answer to this question?
1965
Why is this the correct answer?
The sum of the first 80 natural numbers is \(\frac{80\times81}{2}=3240\), and the sum of the first 50 natural numbers is \(\frac{50\times51}{2}=1275\). Therefore, the required difference is \(3240-1275=1965\). Equivalently, it is the sum of the integers from 51 to 80. Exam tip: use \(n(n+1)/2\) carefully for both sums to avoid a close error such as 1975.
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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