Find the sum of natural numbers from (51) to (75).
Answer and explanation
Correct answer: 1575
There are \(75-51+1=25\) terms from 51 to 75, inclusive. This is an arithmetic sequence with first term 51 and last term 75. Hence, the sum is \(\frac{25}{2}(51+75)=\frac{25}{2}\times126=1575\). Therefore, option A is correct. An answer such as 1600 can result from an error in counting the terms or finding the average. Exam tip: always add \(+1\) when counting terms from one inclusive endpoint to another.
Frequently asked questions
What is the correct answer to this question?
1575
Why is this the correct answer?
There are \(75-51+1=25\) terms from 51 to 75, inclusive. This is an arithmetic sequence with first term 51 and last term 75. Hence, the sum is \(\frac{25}{2}(51+75)=\frac{25}{2}\times126=1575\). Therefore, option A is correct. An answer such as 1600 can result from an error in counting the terms or finding the average. Exam tip: always add \(+1\) when counting terms from one inclusive endpoint to another.
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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