What is the sum of (86+87+88+\cdots+140)?
Answer and explanation
Correct answer: 6215
This is an arithmetic sequence from 86 to 140. The number of terms is \(140-86+1=55\), with first term 86 and last term 140. Therefore, the sum is \(\frac{55}{2}(86+140)=\frac{55}{2}\times226=6215\). A value such as 6185 can result from an error in counting the terms or finding the average. Exam tip: for consecutive integers, always use \(n=\text{last}-\text{first}+1\).
Frequently asked questions
What is the correct answer to this question?
6215
Why is this the correct answer?
This is an arithmetic sequence from 86 to 140. The number of terms is \(140-86+1=55\), with first term 86 and last term 140. Therefore, the sum is \(\frac{55}{2}(86+140)=\frac{55}{2}\times226=6215\). A value such as 6185 can result from an error in counting the terms or finding the average. Exam tip: for consecutive integers, always use \(n=\text{last}-\text{first}+1\).
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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