What is the sum of (46+47+48+\cdots+90)?
Answer and explanation
Correct answer: 3060
This is an arithmetic sequence with first term 46, last term 90, and \(90-46+1=45\) terms. Therefore, \(S=\frac{45}{2}(46+90)=\frac{45}{2}\times136=3060\). Option 4095 is the sum from \(1\) to \(90\), so it incorrectly includes the terms from \(1\) to \(45\). Exam tip: while counting consecutive integers from one endpoint to another, always add \(1\).
Frequently asked questions
What is the correct answer to this question?
3060
Why is this the correct answer?
This is an arithmetic sequence with first term 46, last term 90, and \(90-46+1=45\) terms. Therefore, \(S=\frac{45}{2}(46+90)=\frac{45}{2}\times136=3060\). Option 4095 is the sum from \(1\) to \(90\), so it incorrectly includes the terms from \(1\) to \(45\). Exam tip: while counting consecutive integers from one endpoint to another, always add \(1\).
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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