A student added numbers from (1) to (175) and then subtracted the sum from (1) to (125). What will be the result?
Answer and explanation
Correct answer: 7525
Let the sum of the first n natural numbers be \(S_n=\frac{n(n+1)}{2}\). Therefore, the required result is \(S_{175}-S_{125}=\frac{175\times176}{2}-\frac{125\times126}{2}=15400-7875=7525\). It is also the direct sum of the numbers from 126 to 175. An option such as 7475 results from an error in evaluating a sum or subtraction. Exam tip: the difference of two sums with the same starting term equals the sum of the remaining consecutive terms.
Frequently asked questions
What is the correct answer to this question?
7525
Why is this the correct answer?
Let the sum of the first n natural numbers be \(S_n=\frac{n(n+1)}{2}\). Therefore, the required result is \(S_{175}-S_{125}=\frac{175\times176}{2}-\frac{125\times126}{2}=15400-7875=7525\). It is also the direct sum of the numbers from 126 to 175. An option such as 7475 results from an error in evaluating a sum or subtraction. Exam tip: the difference of two sums with the same starting term equals the sum of the remaining consecutive terms.
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.
