What is the sum of natural numbers from (25) to (75)?
Answer and explanation
Correct answer: 2550
There are \(75-25+1=51\) terms from 25 to 75. These numbers form an arithmetic progression, so their sum is \(\frac{51}{2}(25+75)=\frac{51}{2}\times100=2550\). The option 2500 results from not using the number of terms or the average correctly. Exam tip: for an inclusive range from \(a\) to \(b\), always use \(b-a+1\) terms.
Frequently asked questions
What is the correct answer to this question?
2550
Why is this the correct answer?
There are \(75-25+1=51\) terms from 25 to 75. These numbers form an arithmetic progression, so their sum is \(\frac{51}{2}(25+75)=\frac{51}{2}\times100=2550\). The option 2500 results from not using the number of terms or the average correctly. Exam tip: for an inclusive range from \(a\) to \(b\), always use \(b-a+1\) 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.
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